ISYE 3770 Final test DRV(Quizzes & solns) 24/25 |BRAND NEW |CODE 22

Discrete random variables take on values across a continuum. - answer-FALSE The probability mass function of a discrete random variable is a description of the probabilities associated with each possible value of the random variable. - answer-TRUE The sum of all of the probabilities in a probability mass function equals unity. - answer-TRUE A probability mass function, f(x), is a non-decreasing function of x. - answer-FALSE True or False? P(X = 3) can be written as P(X = 3) = {P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)} - {P(X = 0) + P(X = 1) + P(X = 2)} - answer-TRUE The cumulative distribution function, F(x), 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. - answer-TRUE A cumulative distribution function can be used to find the probability mass function of a discrete random variable. - answer-TRUE If a random variable, X, has only integer values, then the mean, E(X), will always be an integer. - answer-FALSE The mean of a discrete random variable is its expected value. - answer-TRUE If the variances of two discrete random variables are equal, then the means are equal. - answer-FALSE The standard deviation of a discrete random variable is the square of its variance. - answer-FALSE True or False? X, the face value for the throw of a fair die, has the discrete uniform distribution. - answer-TRUE A discrete uniform random variable has equal probability assigned to each of its possible values. - answer-TRUE How many numerical values can a Binomial random variable, X, have? - answer-n+1 True or False? If X is a Binomial random variable, then we can also obtain the mean and variance using the following equations from section 3-3 - answer-TRUE A Bernoulli trial is a random experiment with only two outcomes, success and failure. - answer-TRUE The binomial distribution arises from a series of Bernoulli trials. - answer-TRUE The variance of a binomial random variable with parameters n and p is p(1 - p). - answer-FALSE Which of the following definitions of X demonstrates that X has the Geometric Distribution? - answer-NONBINARY answers True or False? If X is a Geometric random variable, then we can also obtain the mean and variance using the following equations from section 3-3: - answer-TRUE If X is the number of independent Bernoulli trials until the first success, the distribution of X is geometric. - answer-TRUE The distribution of the number of Bernoulli trials until the rth success is the negative binomial distribution. - answer-TRUE The negative binomial distribution has mean r/p. - answer-TRUE The hypergeometric distribution is associated with sampling without replacement from a finite population of N objects. - answer-TRUE If X is a hypergeometric random variable with parameters n, K, and N, and p = K/N, then the number of successes and the total number of objects are: - answer-K and N. When the sample size, n, is large relative to the population size, N, the binomial distribution can adequately approximate the hypergeometric distribution. - answer-FALSE The Poisson distribution is widely used as a model of the number of events in an interval. - answer-TRUE In a Poisson Process, the probability of an event in an interval depends on the length of the interval, but not the location of the interval. - answer-TRUE If the random variable, X, has a Poisson distribution with a mean of 4 events per minute, the mean number of events per hour is: - answer-none of the above For a Poisson process, if the probability that no events occur in a single interval is p, then the probability that an event occurs in an interval four times as long is: - answer-none of the above