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Reading and Comprehension Questions for Chapter 3 1. Discrete random variables take on values across a continuum. True False False – see Section 3-1. 2. The probability distribution of a discrete random variable is a description of the probabilities associated with each possible value of the random variable. True False True – see Section 3-2. 3. The sum of all of the probabilities in a probability mass function equals unity. True False True – see Section 3-2. 4. The cumulative distribution function of a discrete random variable is the sum of all of the probabilities that are less than or equal to x, where x is a specific value of the discrete random variable X. True False True – see Section 3-3. 5. A cumulative distribution function can be used to find the probability mass function of a discrete random variable. True False True – see Section 3-3. 6. The mean of a discrete random variable is its expected value. True False True – see Section 3-4. 7. The variance of a discrete random variable is its expected value True False False – see Section 3-4. 8. The standard deviation of a discrete random variable is the square of its variance. True False False – see Section 3-4. 9. A discrete uniform random variable has equal probability assigned to each of its possible values. True False True – see Section 3-5. 10. If X is a discrete uniform random variable defined on the consecutive integers 10, 11, …, 20, the mean of X is: a. 30 b. 15 c. 12 d. None of the above Answer is b – see Equations 3.6. 11. A Bernoulli trial is a random experiment with only two outcomes, success and failure. True False True – see Section 3-6. 12. The binomial distribution arises from a series of Bernoulli trials. True False True – see Section 3-6. 13. If X is a binomial random variable with n = 20 and p = 0.25, the mean of X is: a. 10 b. 5 c. 4 d. None of the above Answer is b – see Equations 3.8 14. The variance of a binomial random variable with parameters n and p is p(1 – p). True False False – see Equations 3.8 15. If X is the number of independent Bernoulli trials until the first success, the distribution of X is geometric. True False True – see Section 3-7.1. 17. The distribution of the number of Bernoulli trials until the rth success is the negative binomial distribution. True False False – see Section 3-7.2. 18. The negative binomial distribution has a lack-of memory property. True False False – the lack of memory property is associated with the geometric distribution; see Section 3-7.1. 19. The hypergeometric distribution is associated with sampling without replacement from a finite population of N objects. True False True – see Section 3-8. 20. If X is a hypergeometric random variable with parameters n, K, and N, and p = K/N, the mean and variance of X are: a. np and np(1 – p) b. p and np(1 – p) c. np and p(1 – p) d. np and np(1 – p)[(N – n)/(N – 1)] Answer is d; see Equations 3-14. 21. When the sample size n is large relative to the population size N, the binomial distribution can adequately approximate the hypergeometric distribution. True False False – the binomial distribution can adequately approximate the hypergeeometric distribution when n is small relative to N. 22. The Poison distribution is a limiting form of the binomial distribution. True False True - see Section 3-9. 23. The Poisson distribution is widely used as a model of the number of events in an interval. True False True - see Section 3-9. 24. The mean and variance of the Poisson distribution are both equal to the parameter of the distribution, λ. True False True - see Section 3.9.