Class Assignment (#5 – 11am class/ #6 -- 10 am class)
Group Assignment
1. USA Today reported that approximately 25% of all state prison inmates released on parole become repeat offenders while on parole. Suppose the parole board is examining five prisoners up for parole. Let r.v. X = number of prisoners out of five on parole who become repeat offenders. The probability distribution for r.v. X is shown below:
X / 0 / 1 / 2 / 3 / 4 / 5P(X=x) / 0.237 / 0.396 / 0.264 / 0.088 / 0.015 / 0.001
a) What type of random variable is being investigated here?
b) Is the probability distribution valid? How do you know?
c) Sketch the probability histogram for random variable X.
d) Find the probability that at least one of the five parolees will be repeat offenders
e) Find the probability that the number of the five parolees will be repeat offenders is more than one
f) How many parolees would we expect to be repeat offenders out of 5? (we are looking for the “mean” of the random variable here; also called the “expected value”).
2. A number between 0 and 10 is generated randomly. Assuming that any real number between 0 and 10 (inclusive) has the same chance of occurring implies the random number (Y) follows the Uniform distribution.
For a single number generated at random, find the following probabilities. Show a sketch with the appropriate region shaded for parts a-d.
a. P(Y < 1)
c. P(3.25 < Y < 7.5)
d. P(Y > 9.5)
e. Suppose 2 numbers are generated randomly (independent of each other). What is the probability that both numbers are greater than 9.5?