Download Discrete Random Variables

PSTAT 5E
Discrete Random Variables
1. The probability function for the number of insurance policies Timmy will sell to a customer
is given by f(x) = 0.5 – (x/6) for x = 0, 1, and 2.
A. Is this a valid probability function? Explain.
B. What is the probability Timmy will sell exactly 2 insurance policies to a customer?
C. What is the expected number of insurance policies Timmy will sell?
2. The number of defects, X, in a new car from a certain manufacturer has the following pdf:
k
P(X = k)
0
0.5
1
0.15
2
3
0.05
A. Find the probability there are exactly 2 defects.
B. Find the probability there are at most 1 defect in a new car.
C. Find the standard deviation for the number of defects in a new car.
3. If electrical power failures occur according to a Poisson distribution with an average of 3
failures every 20 weeks, calculate the probability that there will be no more than one
failure during any particular week.
4. A box contains 6 Red and 8 Blue marbles. Two marbles are withdrawn randomly. If they
are the same color, then you win $1.10; if they are different colors, then you lose $1.
Calculated the expected value and standard deviation of the amount of money you win.
5. A lottery game chooses three digits from 0 to 9 where each number is chosen
independently (assume with replacement).
A. What is the probability that the number 196 will be the winning number tomorrow?
B. If Timmy plays the number 196 for 100 days, what is the probability that he will
win more than once?
C. If Timmy plays the number 196 for 300 days, what is the expected number of
times he will win?
6. Suppose you pay $10 to play a game. Two dice are rolled. If you roll “doubles”, then you
win $75; otherwise you win nothing.
A. What is your expected gain or loss per game?
B. What would you expect to happen if you played this game 1000 times? Would this
be a good “investment”?
7. A random sample of 9 people is taken from a population in which 30% favor a particular
political stand. What is the probability that exactly 6 individuals in the sample favor this
political stand? Check all necessary conditions.