Questions and Answers
What formula is used to calculate the probability of having 4 heads in 5 tosses using a coin?
(n! / [r! (n - r)!]) * (p^r) * (q^(n-r))
Which parameter defines the mean value in a Normal Distribution?
Median
What concept does the Weibull distribution model specifically focus on?
Time to failure for components
What characteristic is associated with a process described as 'memoryless'?
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In a Discrete or Continuous Uniform distribution, what type of uncertainty is represented?
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What does the selected range from -Infinity to +Infinity signify in a Normal Distribution?
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What is the formula for calculating the Z-score in a standard normal distribution?
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If a distribution is asymmetrical, what measure describes the asymmetry?
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Which measure describes the tailedness of a distribution and how often outliers occur?
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In a Bernoulli experiment, how many possible outcomes does each trial have?
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What does the Binomial Distribution calculate in a series of trials?
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What property differentiates a Binomial Distribution from other distributions?
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What is the formula to calculate the expected value of a random variable?
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In the context of random variables, what does the variance measure?
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What does the standard deviation represent in terms of a random variable's distribution?
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Which type of average corresponds to 'The Favourite Average' in a given data set?
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Which mean can be calculated by dividing the total number of terms by the sum of their reciprocal values?
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What does the variance formula take into account when calculating the spread of a random variable's outcomes?
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Study Notes
Probability and Statistics
- The binomial probability formula is:
P(X = r) = [n! / (r!(n-r)!)] * p^r * q^(n-r), wherenis the number of trials,ris the number of successes,pis the probability of success, andqis the probability of failure.
Random Variables
- A random variable is a real number assigned to every possible outcome or event in an experiment.
- Examples of random variables include checking 50 questionnaires, sending 2,000 written letters, building an annex for the IT building in 6 months, and testing the lifetime of LCD bulbs.
Expected Value and Variance
- The expected value
E(X)is calculated as:Σ Xi P(Xi)wherei = 1 to n. - The variance
σ2is calculated as:Σ [Xi – E(X)] 2 P(Xi)wherei = 1 to n. - The standard deviation
σis the square root of the variance.
Types of Distributions
- Normal distribution: a continuous probability distribution with a symmetric bell-shaped curve.
- Lognormal distribution: a probability distribution of a random variable whose logarithm is normally distributed.
- Exponential distribution: a continuous probability distribution that models the time between independent events in a process.
- Weibull distribution: a continuous probability distribution that models the time to failure of a component.
- Discrete or Continuous Uniform distribution: models complete uncertainty, where all outcomes are equally likely.
- Triangular distribution: models a process when only the minimum, most-likely, and maximum values are known.
Measures of Central Tendency
- Mean: the average of a set of values, calculated by adding all values and dividing by the total count.
- Median: the middle value in a set of values when arranged in order from lowest to highest.
- Mode: the most frequent value in a set of values.
Skewness and Kurtosis
- Skewness: a measure of the asymmetry of a distribution, where a distribution is asymmetrical if its left and right sides are not mirror images.
- Kurtosis: a measure of the tailedness of a distribution, which describes how often outliers occur.
