AP POLYCET MATHEMATICS Multiple Choice Questions (MCQs)

AP POLYCET Mathematics - Random Variables and Distribution Multiple Choice Questions (MCQs)

106. What is a random variable?
     a) A variable that is determined by the values of other variables
     b) A variable whose value is determined by chance
     c) A constant value
     d) A variable with a fixed value
     Answer: b) A variable whose value is determined by chance
107. Which of the following is a discrete random variable?
     a) The height of a person
     b) The number of cars in a parking lot
     c) The weight of a person
     d) The time taken for a bus to arrive
     Answer: b) The number of cars in a parking lot
108. Which distribution is associated with a random variable having two possible outcomes (success/failure)?
     a) Normal distribution
     b) Binomial distribution
     c) Poisson distribution
     d) Uniform distribution
     Answer: b) Binomial distribution
109. What is the mean of a probability distribution?
     a) The middle value of the distribution
     b) The average of all possible outcomes
     c) The most frequent outcome
     d) The least probable outcome
     Answer: b) The average of all possible outcomes
110. In a uniform distribution, what is the probability of each outcome?
     a) Varies with the values
     b) Constant for all outcomes
     c) Zero
     d) Increases with the number of trials
     Answer: b) Constant for all outcomes
111. What is the range of a random variable?
     a) The sum of all possible outcomes
     b) The difference between the maximum and minimum values
     c) The average of all outcomes
     d) The square of the largest value
     Answer: b) The difference between the maximum and minimum values
112. Which of the following is a continuous random variable?
     a) The number of defective items in a batch
     b) The number of students in a class
     c) The weight of a person
     d) The number of heads in a coin toss
     Answer: c) The weight of a person
113. In a binomial distribution, which of the following parameters must be fixed?
     a) The number of successes
     b) The number of trials
     c) The probability of failure
     d) The sample size
     Answer: b) The number of trials
114. What is the expected value of a discrete random variable?
     a) The sum of all values
     b) The weighted average of all values, weighted by their probabilities
     c) The most frequent value
     d) The least frequent value
     Answer: b) The weighted average of all values, weighted by their probabilities
115. What is the variance of a probability distribution?
     a) The difference between the highest and lowest values
     b) The square of the standard deviation
     c) The square root of the expected value
     d) The average of the values
     Answer: b) The square of the standard deviation
116. In a Poisson distribution, which parameter defines the average number of occurrences in a fixed interval?
     a) Mean
     b) Standard deviation
     c) Lambda (λ)
     d) Variance
     Answer: c) Lambda (λ)
117. What is the characteristic of a normal distribution?
     a) The distribution is skewed to the left
     b) The distribution is symmetric around the mean
     c) The distribution is bimodal
     d) The distribution is discrete
     Answer: b) The distribution is symmetric around the mean
118. What does the Central Limit Theorem state about random variables?
     a) The distribution of the sum of random variables approaches a normal distribution as the sample size increases
     b) The distribution of random variables is always normal
     c) The sample mean always equals the population mean
     d) The mean of the sample decreases with the sample size
     Answer: a) The distribution of the sum of random variables approaches a normal distribution as the sample size increases
119. What is the standard deviation in a normal distribution?
     a) A measure of the spread of the distribution
     b) The average value of all observations
     c) The middle value of the distribution
     d) A measure of the skewness of the distribution
     Answer: a) A measure of the spread of the distribution
120. What does the probability density function (PDF) of a continuous random variable describe?
     a) The probability that the random variable takes on any specific value
     b) The probability that the random variable is less than or equal to a specific value
     c) The shape of the probability distribution
     d) The expected value of the random variable
     Answer: c) The shape of the probability distribution

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