After scoring a touchdown, a football team may elect to attempt a two-point conversion, by running or passing the ball into the end zone. If successful, the team scores two points. For a certain football team, the probability that this play is successful is 0.40.
a. Let X = 1 if successful, X = 0 if not. Find the mean and variance of X.
b. If the conversion is successful, the team scores 2 points; if not the team scores 0 points. Let Y be the number of points scored. Does Y have a Bernoulli distribution? If so, find the success probability. If not, explain why not.
c. Find the mean and variance of Y.
(a) Bernoulli (p), where 
.
(b) No. A Bernoulli random variable has possible values 0 and 1. The possible values of Y are 0 and 2.
(c) Y = 2X, where X ~ Bernoulli (p).
Therefore 
.
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