Question

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.

1. Let X = 1 if successful, X = 0 if not. Find the mean and variance of X.

Answer 1

a) Mean(x) = 0.40

b) Variance(x) = 0.24

Explanation:

From the information given, the process is Bernoulli process, since the team can run or pass the ball into the end zone to score two points only. We are not told the number of times. Thus, n is unknown. That is, we are not told how many times the team successfully pass the ball into the end zone.

By Bernoulli process, the mean and variance are given as follow:

Mean = p

Variance = pq. This is the same as p(1-p)

Where p is the probability that this play is successful and q is the probability that this play is not successful.