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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 0.80.1. Let X = 1 if successful, X = 0 if not. Find the mean and the variance of X. Round the answers to two decimal places.The mean of X is = .The variance of X is =2. Let Y be the number of points scored. Find the mean and variance of Y. Round the answers to two decimal places.The mean of Y is =The variance of Y is =

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Answer:

Step-by-step explanation:

given that 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.

X=1 if successful and

X=0 if not

pdf of X is

X      1       0

p    0.8   0.2

E(x) = [tex]1(0.8)+0(0.2)\\=0.8[/tex]

[tex]E(x^2) = 1^2(0.8) = 0.8[/tex]

Var(x) = 0.8-0.8*0.8

= 0.16

Now let us consider Y.

Y is the no of points scored.

Y      2       0

p     0.8    0.2

E(Y) = [tex]2(0.8)+0(0.2)\\=1,.6[/tex]

[tex]2^2(0.8)+0(0.2)\\= 3.2[/tex]

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