Exam 7: Random Variables and Discrete Probability Distributions

For a discrete probability distribution to be valid, the probabilities must lie between 0 and 1, where the sum of all probabilities must be 1.

Which probability distribution is appropriate when the events of interest occur randomly, independently of one another, and rarely?

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

Which of the following cannot generate a Poisson distribution?

Historical data collected at the Commonwealth Bank in Sydney revealed that 80% of all customers applying for a loan are accepted. Suppose that 50 new loan applications are selected at random. a. Find the expected value and the standard deviation of the number of loans that will be accepted by the bank. b. What is the probability that at least 42 loans will be accepted? c. What is the probability that the number of loans rejected is between 10 and 15, inclusive?

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

The standard deviation of a binomial distribution for which n = 100 and p = .35 is:

The proprietor of a small hardware store employs three men and three women. He will select three employees at random to work on Christmas Eve. Let X represent the number of women selected. a. Express the probability distribution of X in tabular form. b. What is the probability that at least two women will work on Christmas Eve?

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 .

For each of the following random variables, indicate whether the variable is discrete or continuous, and specify the possible values that it can assume. a. X = The number of animals visited by a veterinarian in one day. b. X = Closing share price of a particular stock over one month. c. X = The weights of new members at a gymnasium. d. X = The number of students attending a lecture, where the theatre seats 250 people. e. X = The temperature at a seaside resort in the summer.