Exam 7: Random Variables and Discrete Probability Distributions

Let X be a Poisson random variable with $\mu$ = 6. Use the table of Poisson probabilities to find: a. P(X $\le$ 8) b. P(X = 8) c. P(X $\le$ 5) d. P(6 $\le$ X $\le$ 10)

Gender is an example of a continuous random variable.

Given a binomial random variable with n = 20 and p = 0.6, find the following probabilities using the binomial table. a. P(X $\le$ 13). b. P(X $\ge$ 15). c. P(X = 17). d. P(11 < X < 14).

Let X represent the number of computers in Australian households who own computers. The probability distribution of X is as follows: x 1 2 3 4 5 p(x) .25 .33 .17 .15 .10 What is the probability that a randomly selected Australian household will have: a. more than 2 computers? b. between 2 and 5 computers, inclusive? c. fewer than 3 computers?

Let X be a Poisson random variable with $\mu$ = 8. Use the table of Poisson probabilities to find: a. P(X $\le$ 6). b. P(X = 4). c. P(X $\ge$ 3). d. P(9 $\le$ X $\le$ 14).

Phone calls arrive at the rate of 30 per hour at the reservation desk for a hotel. a. Find the probability of receiving two calls in a five-minute interval of time. b. Find the probability of receiving exactly eight calls in 15 minutes. c. If no calls are currently being processed, what is the probability that the desk employee can take a four-minute break without being interrupted?

A bivariate distribution is a distribution is a joint probability distribution of two variables.

The probability distribution for X is as follows: x -1 0 1 2 p(x) 0.1 0.25 0.55 0.1 Find the expected value of Y = X + 10.

An official from the Australian Securities and Investments Commission estimates that 75% of all investment bankers have profited from the use of insider information. If 15 investment bankers are selected at random from the Commission's registry, find the probability that: a. at most 10 have profited from insider information. b. at least six have profited from insider information. c. all 15 have profited from insider information.

The probability distribution for X is as follows: x -1 0 1 2 p(x) 0.1 0.25 0.55 0.1 a. Find E[5X + 1]. b. Find V[5X + 1].

A Poisson distribution with $\mu$ = .60 is a:

The number of accidents that occur annually on a busy stretch of highway is an example of:

A discrete random variable can take either finite or infinite values as long as the values are countable.

The lottery commission has designed a new instant lottery game. Players pay $1.00 to scratch a ticket, where the prize won, X, (measured in $) has the following discrete probability distribution : X P[X] 0 0.95 10 0.049 100 0.001 Which of the following best describes the standard deviation of X ? A. 14.552 in B. 3.815 in \ C. 0.348 in \ D. None of these choices are correct

Which probability distribution is appropriate when the events of interest occur randomly, independently of one another, and rarely? A. Binomial distribution. B. Poisson distribution. C. Any discrete distribution. D. Any continuous distribution.

A market researcher selects 20 students at random to participate in a wine-tasting test. Each student is blindfolded and asked to take a drink out of each of two glasses, one containing an expensive wine and the other containing a cheap wine. The students are then asked to identify the more expensive wine. If the students have no ability whatsoever to discern the more expensive wine, what is the probability that the more expensive wine will be correctly identified by: a. more than half of the students? b. none of the students? c. all of the students? d. eight of the students?

Consider a binomial random variable X with n = 7 and p = 0.3. a. Find the probability distribution of X. b. Find P(X < 3). c. Find the mean and the variance of X.

Let X and Y be two independent random variables with the following probability distributions: x 1 2 3 p(x) 0.2 0.5 0.3 y -1 0 1 p(y) 0.3 0.3 0.4 Find the probability distribution of the random variable X + Y.

The Binomial distribution and the Poisson distribution are discrete bivariate distributions.

The lottery commission has designed a new instant lottery game. Players pay $1.00 to scratch a ticket, where the prize won, X, (measured in $) has the following discrete probability distribution : X P[X] 0 0.95 10 0.049 100 0.001 Which of the following best describes the expected value of X ?