## Transcribed Text

1. The random variable X has a binomial distribution with E(X)=7.5 and Var(X)=5.25. Find n and p
for this distribution.
2. Suppose X is a binomial random variable with n=10 and p=0.1. Feel free to use a computer to
answer the following:
a) P(X=0)
b) P(X=2)
c) P(X<2)
d) P(X>8)
e) E(X)
f) Var(X)
3. A survey on British Social Attitudes asked respondents if they had ever boycotted goods for
ethical reasons (Statesman, January 28, 2008). The survey found that 23% of the respondents
have boycotted goods for ethical reasons. Using the binomial distribution (and a computer if you
want), answer the following questions.
a) In a sample of six British citizens, what is the probability that two have ever boycotted goods
for ethical reasons?
b) In a sample of six British citizens, what is the probability that at least two respondents have
boycotted goods for ethical reasons?
c) In a sample of ten British citizens, what is the probability that none have boycotted goods for
ethical reasons?
d) In a sample of ten British citizens, what is the expected number of people that have
boycotted goods for ethical reasons?
4. The joint probability mass function of random variables X and Y is given by
Are X and Y independent? Justify your answer
5. A large insurance agency services a number of customers who have purchased both a
homeowner's policy and an automobile policy from the agency. For each type of policy, a
deductible amount must be specified. For an automobile policy, the choices are $100 and $250,
whereas for a homeowner's policy, the choices are 0, $100, and $200.
Suppose an individual with both types of policy is selected at random from the agency's files.
Let
X = the deductible amount on the auto policy, and
Y = the deductible amount on the homeowner's policy.
Suppose the following table represents the joint distribution of X and Y:
a) What are the mean and standard deviation of X?
b) What are the mean and standard deviation of Y?
c) What is the covariance between X and Y?
d) What is the correlation between X and Y?
e) Are X and Y independent? Justify your answer.
6. Suppose a game involves dropping 3 coins on the tableāa nickel, a dime, and a quarter. Each
coin that lands "heads up" you are allowed to keep, so that the possible reward R ranges from 0
to 40c. We found the expected value of R. For this problem, now find Var(R).

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