Engineering Course Outcomes Quiz
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Questions and Answers

Which concept is NOT included in the course objective?

  • Financial accounting (correct)
  • Statistics techniques
  • Random variable
  • Numerical aptitude

Which of the following is a part of Course Outcome CO1?

  • Time-Series analysis (correct)
  • Data visualization
  • Market analysis
  • Financial metrics

Which Program Outcome (PO) relates to the ability to solve complex problems?

  • PO 1
  • PO 6
  • PO 10
  • PO 2 (correct)

In the context of this course, what does CO2 focus on?

<p>Understanding of Probability and Random variables (C)</p> Signup and view all the answers

What skill is NOT expected as part of the Course Outcome CO4?

<p>Data mining techniques (D)</p> Signup and view all the answers

Which of the following outcomes aligns best with modern tool usage?

<p>PO 5 (A)</p> Signup and view all the answers

Which mathematical concepts are included in Course Outcome CO5?

<p>Pipe &amp; Cistern problems (D)</p> Signup and view all the answers

Which Program Outcome emphasizes the importance of ethics in engineering?

<p>PO 8 (A)</p> Signup and view all the answers

Which measure of central tendency is most influenced by extreme values?

<p>Mean (C)</p> Signup and view all the answers

What is the appropriate measure of dispersion to use when evaluating a dataset with outliers?

<p>Interquartile Range (C)</p> Signup and view all the answers

Which probability distribution is used when there are a fixed number of independent trials each with two possible outcomes?

<p>Binomial Distribution (C)</p> Signup and view all the answers

What is the primary application of the central limit theorem?

<p>To establish the distribution of sample means (B)</p> Signup and view all the answers

In hypothesis testing, what does a p-value indicate?

<p>The likelihood of observing the sample data given the null hypothesis (A)</p> Signup and view all the answers

Which of the following is a method for estimating population parameters?

<p>Sample statistics (A)</p> Signup and view all the answers

What is the key difference between discrete and continuous random variables?

<p>Discrete variables can only assume integer values, while continuous variables can assume any value within an interval (C)</p> Signup and view all the answers

Which statistical test is used for comparing means from three or more independent samples?

<p>ANOVA (B)</p> Signup and view all the answers

What is represented by 'n' in the binomial probability distribution?

<p>The total number of trials (B)</p> Signup and view all the answers

Which of the following is NOT an assumption of the binomial distribution?

<p>The probability of success changes with each trial (B)</p> Signup and view all the answers

In the binomial formula P(X = r) = nCr × p^r × q^(n-r), what does 'q' represent?

<p>The probability of failure (A)</p> Signup and view all the answers

Which formula is known as the Recurrence Formula in the context of binomial distribution?

<p>P(r + 1) = P(r) × (n - r)/(r + 1) × p/q (D)</p> Signup and view all the answers

What is the sum of the probabilities 'p' and 'q' in a binomial distribution?

<p>1 (A)</p> Signup and view all the answers

Which of the following distributions is classified as a continuous probability distribution?

<p>Normal Distribution (D)</p> Signup and view all the answers

What does 'r' represent in the binomial probability distribution formula?

<p>The number of successes in trials (A)</p> Signup and view all the answers

Which of the following best describes a discrete probability distribution?

<p>Includes only distinct or separate values (A)</p> Signup and view all the answers

What is the mean of a binomial distribution represented as?

<p>$np$ (D)</p> Signup and view all the answers

Which of the following correctly represents the variance of a binomial distribution?

<p>$npq$ (D)</p> Signup and view all the answers

What does the moment generating function of a binomial distribution about the origin equal?

<p>$(q + pe^t)^n$ (B)</p> Signup and view all the answers

What is the standard deviation of a binomial distribution if its variance is given by $npq$?

<p>$ ext{sqrt}(npq)$ (A)</p> Signup and view all the answers

In a binomial experiment, if the probability of success is $0.3$, what is the probability of failure?

<p>$0.7$ (A)</p> Signup and view all the answers

If a machine produces 10% defective bolts, what is the probability of none being defective out of 10 screws?

<p>$0.3487$ (A)</p> Signup and view all the answers

What application of binomial distribution deals with the reliability of systems?

<p>Estimation of reliability of systems (A)</p> Signup and view all the answers

How would you denote the probability of failure in a binomial distribution?

<p>$q = 1 - p$ (D)</p> Signup and view all the answers

Which of the following combinations of parameters is necessary to apply binomial distribution formulas?

<p>Total trials, probability of success, and probability of failure (B)</p> Signup and view all the answers

What is the expected number of families having 4 boys?

<p>50 (A)</p> Signup and view all the answers

How many persons in a group of 20 are graduates if 4 persons are selected at random and the probability that all are graduates is 0.0016?

<p>4 (A)</p> Signup and view all the answers

Using Poisson distribution, what is the formula to calculate the probability of exactly r occurrences?

<p>$P(X=r) = \frac{e^{-\lambda}\lambda^r}{r!}$ (B)</p> Signup and view all the answers

What does the symbol λ represent in Poisson distribution?

<p>Average number of occurrences (D)</p> Signup and view all the answers

In the recurrence formula for Poisson distribution, which expression correctly relates P(r) and P(r+1)?

<p>$P(r+1) = \frac{\lambda}{r + 1} P(r)$ (B)</p> Signup and view all the answers

What is the mean of the Poisson distribution?

<p>λ (B)</p> Signup and view all the answers

If the probability that a bulb will fuse after 150 days is 0.05, what is the probability that all 5 bulbs will last longer than 150 days?

<p>0.95^5 (D)</p> Signup and view all the answers

What does the variance of Poisson distribution equal?

<p>$\lambda$ (D)</p> Signup and view all the answers

What is the mean of the Poisson distribution calculated from the given data?

<p>0.5 (A)</p> Signup and view all the answers

What is the theoretical frequency for r = 1 in the fitted Poisson distribution?

<p>61 (C)</p> Signup and view all the answers

Which of the following is a property of the normal distribution?

<p>The mean, median, and mode are all equal (A)</p> Signup and view all the answers

In the Poisson distribution provided, what does λ represent?

<p>The mean number of occurrences in a fixed interval (C)</p> Signup and view all the answers

What is the value of the theoretical frequency for r = 2?

<p>15 (C)</p> Signup and view all the answers

Which equation corresponds to the probability density function of a normal random variable?

<p>$f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x - \mu)^{2}}{2\sigma^2}}$ (A)</p> Signup and view all the answers

How is the standard deviation represented in the context of normal distribution?

<p>$\sigma$ (C)</p> Signup and view all the answers

Which of the following statements is NOT true for the Poisson distribution?

<p>It is appropriate for modeling continuous data. (D)</p> Signup and view all the answers

Flashcards

Measures of dispersion

A measure of how spread out data points are from the central tendency (mean, median, or mode). Common examples include standard deviation, variance, and quartile deviation.

Least Squares Principle

A technique for finding the line that best fits a set of data points by minimizing the sum of squared errors.

Regression Analysis

A statistical method used to estimate the relationship between two or more variables. It involves using one variable to predict the value of another.

Probability Distribution

A probability distribution that describes the probability of a random variable taking on a particular value. Common examples include the Normal, Exponential, Binomial, and Poisson distributions.

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Central Limit Theorem

A powerful theorem stating that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the original population distribution.

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Hypothesis Testing

A statistical method used to test hypotheses about population parameters. It involves comparing sample data to a hypothesized value.

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Statistical Inference

A set of procedures used to estimate population parameters based on sample data.

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Least Square Estimation

A method used to estimate the parameters of a statistical model by minimizing the sum of squared errors.

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Correlation

A statistical method used to analyze the strength and direction of the relationship between two or more variables.

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Curve Fitting/Regression Analysis

A statistical technique used to find the best-fitting curve or line to represent a set of data points. It helps us understand the relationship between variables.

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Time-Series Analysis

A way to analyze data that changes over time. It helps us identify patterns, trends, and seasonal variations.

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Estimation of Parameters

A set of procedures used to estimate population parameters based on sample data.

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Central Tendency

A numerical measure that describes the center or typical value of a dataset.

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Binomial Distribution

A probability distribution that describes the probability of a random variable taking on a particular value. It assumes that the number of trials is finite, each trial has two possible outcomes, and the probability of success is constant across all trials.

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Continuous Probability Distribution

A type of probability distribution where the variable can take on any value within a certain range. Examples include the Normal, t, and F distributions.

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Recurrence Formula

A formula that helps to calculate the probability of a specific number of successes in a binomial distribution. It relates the probability of 'r' successes to the probability of (r+1) successes.

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Discrete Probability Distribution

A type of probability distribution where the variable can only take on discrete values. Examples include the Binomial and Poisson distributions.

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Poisson Distribution

This distribution describes the probability of a specific number of events occurring in a fixed interval of time or space, when the events occur independently and at a constant average rate.

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Normal Distribution

The most common continuous probability distribution, shaped like a bell curve. Many natural phenomena and data sets follow this distribution.

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t-Distribution

A distribution used for inference when the population standard deviation is unknown. It is similar to the normal distribution but adjusted for smaller sample sizes.

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F-Distribution

A distribution used to compare variances of two populations. It involves the ratio of two variances.

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Mean of Binomial Distribution

The average value of a binomial random variable. It represents the expected number of successes in a fixed number of trials.

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Variance of Binomial Distribution

The spread of a binomial distribution around its mean. It measures how much the values deviate from the average.

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Moment Generating Function of Binomial Distribution

A mathematical function that summarizes the probability distribution of a random variable. It's useful for studying moments of the distribution.

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Applications of Binomial Distribution

A statistical technique that uses the binomial distribution to analyze real-world scenarios involving a set of independent trials with two possible outcomes.

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Probability Formula for Binomial Distribution

The probability of exactly 'r' successes in 'n' independent trials, where each trial has a probability 'p' of success and 'q' of failure.

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Combination (nCr)

The number of ways to choose a group of 'r' objects out of a total of 'n' objects, without regard to order.

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Probability of Success (p)

The probability of success in a single trial in a binomial distribution.

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Probability of Failure (q)

The probability of failure in a single trial in a binomial distribution.

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Number of Trials (n)

The number of independent trials in a binomial distribution.

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Poisson Probability Formula

A formula used to calculate the probability of observing a specific number of events (r) in a Poisson distribution given the average rate of events (λ).

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Poisson Recurrence Formula

A relationship between the probabilities of consecutive occurrences in a Poisson distribution. It states that the probability of observing (r+1) events can be calculated by multiplying the probability of observing (r) events by the average rate (λ) and dividing by (r+1).

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Mean of Poisson Distribution

The expected value of a Poisson distribution, representing the average number of events that occur within a given interval.

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Variance of Poisson Distribution

A measure of the spread of the Poisson distribution. It is equal to the average rate (λ) of the distribution. In a Poisson distribution, the variance and mean are always equal.

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Number of Events (r)

The number of events that occur within a specified time or space interval, used in the Poisson distribution.

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Average Rate (λ)

The average rate of events occurring within a specified time or space interval. It is a key parameter in the Poisson distribution.

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Assumptions of Poisson Distribution

The Poisson distribution applies to random events that occur independently at a constant average rate. This means that the occurrence of one event does not affect the probability of another event occurring.

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λ (Lambda) in Poisson Distribution

The average number of events occurring in a specific time interval in a Poisson distribution.

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P(r) in Poisson Distribution

The probability of observing exactly 'r' events in a specified time interval for a Poisson distribution.

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Frequency Distribution

A representation of data that describes how often each value occurs in a dataset.

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Theoretical Frequencies

A frequency distribution that describes how often each value occurs in a dataset that follows a Poisson distribution.

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Probability Density Function (PDF) for Normal Distribution

The probability density function for a normally distributed random variable.

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Total Area under Normal Curve

The total area under the normal distribution curve, which always equals 1.

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Study Notes

Course Information

  • Course Title: Statistics & Probability
  • Course Code: BAS0303
  • Instructor: Dr. Anil Agarwal
  • Department: Mathematics
  • Semester: B.Tech 3rd
  • Date: 12/13/2024

Unit III: Probability Distribution

  • Topic Objective (CO3): Probability distributions are essential for making predictions and estimates in research.

  • Probability Distributions: Categorized as discrete or continuous.

  • Discrete: Binomial, Poisson

  • Continuous: Normal, Exponential

  • Binomial Distribution (CO3): Used when a process has only two outcomes (success or failure) repeated a fixed number of times.

    • Key characteristic: Fixed number of trials, independent trials, and constant probability of success.

  • Poisson Distribution (CO3): Used to model the probability of a certain number of events occurring within a given time or space.

    • Key characteristic: Independent events in fixed space or time intervals.

  • Normal Distribution (CO3): A continuous probability distribution used widely.

    • Characteristics: Symmetrical about its mean, described by mean and standard deviation, major component in statistical inference.

  • Exponential Distribution (CO3): Models the time until an event occurs in a process with a constant rate.

Evaluation Scheme

  • Detailed breakdown of evaluation scheme provided.
  • Includes different components like lectures, assignments, quizzes, practical/lab components and sessionals/university exams.

Branch-wise Applications

  • Data Analysis
  • Artificial Intelligence
  • Digital Communication (Information theory and coding)

Course Objectives

  • Students will be familiarized with Statistical techniques, probability distribution, Hypothesis testing, ANOVA, and numerical aptitude.
  • Develop skills to apply these concepts and mathematical tools in their respective disciplines.

Program Outcomes (POs)

  • Detailed list of Program Outcomes (POs) for the course.

CO-PO Mapping

  • Table showing the mapping of Course Outcomes (COs) to Program Outcomes (POs).
  • Includes levels of mapping (Low, Medium, High)

Program Specific Outcomes (PSOs)

  • Explicit statement of the Program Specific Outcomes (PSOs)
  • Clear description of the learning expectations of educational institutions in teaching specific knowledge and skills to their students.

Program Educational Objectives (PEOs)

  • Statement of Program Educational Objectives, outlining broader goals for the program's graduates.

Unit Objectives

  • Basic knowledge in probability theory.
  • Students learn applied mathematical methods.
  • Gain understanding of probability and how it is applied in business.
  • Computing probability of "success" when repeated.
  • Using Poisson distributions for occurrence prediction.
  • Familiarity with characteristics of Normal curves.
  • Exploring properties of Random Variables.

Topic Objectives

  • Probability distributions make valuable predictions and allow for analysis to support further investigation.

Topic Video Links & Resources

  • Provided list of YouTube and NPTEL videos related to course topics.

Daily Quiz(CO3)

  • Sample problems related to probability calculations.

Weekly Assignments(CO3)

  • Practical problems related to probability distributions.

Recap of Unit III

  • Key topics covered, emphasizing probability distributions, Binomial, Poisson, Normal, and Exponential distributions.

References:

  • Lists of resources and textbooks used in the course.

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S & P Unit-III PDF

Description

Test your knowledge on the Course Outcomes and Program Outcomes specific to engineering. This quiz covers various concepts including measures of central tendency, hypotheses testing, and program outcomes related to problem-solving and ethics. Assess your understanding of key statistical methods and their applications.

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