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</p> Signup and view all the answers

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

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

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

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

    Which mathematical concepts are included in Course Outcome CO5?

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

    Which Program Outcome emphasizes the importance of ethics in engineering?

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

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

    <p>Mean</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</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</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</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</p> Signup and view all the answers

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

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

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

    <p>ANOVA</p> Signup and view all the answers

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

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

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

    <p>1</p> Signup and view all the answers

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

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

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

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

    Which of the following best describes a discrete probability distribution?

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

    What is the mean of a binomial distribution represented as?

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

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

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

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

    <p>$(q + pe^t)^n$</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)$</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>$0.7$</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>$0.3487$</p> Signup and view all the answers

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

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

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

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

    What is the expected number of families having 4 boys?

    <p>50</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</p> Signup and view all the answers

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

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

    What does the symbol λ represent in Poisson distribution?

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

    What is the mean of the Poisson distribution?

    <p>λ</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</p> Signup and view all the answers

    What does the variance of Poisson distribution equal?

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

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

    <p>0.5</p> Signup and view all the answers

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

    <p>61</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</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</p> Signup and view all the answers

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

    <p>15</p> Signup and view all the answers

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

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

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

    <p>$\sigma$</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.</p> Signup and view all the answers

    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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    Related Documents

    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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