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 prob- ability that this play is successful is 0.40.
Let X=1 if succfull, X=0 if not, Find the mean and variance of X

Answer 1

Answer:

Mean = 0.4

Variance = 0.24    

Step-by-step explanation:

We are given the following in the question:

Possible outcomes:

X = 1(success)

X = 0(Fail)

Probability of success = p = P(X = 1) = 0.40

Since there are only two possible outcome, it follows a Bernoulli's distribution where the probability density function is given by:

$p(x) = p, ~x = 1\\~~~~~~=1-p,~ x = 0$

The mean of distribution is:

$\mu = p\\\mu = 0.4$

The variance of distribution is:

$\sigma^2 = p(1-p) = 0.4(1-0.4)\\\sigma^2 = 0.24$