The number of home runs scored by a certain team in one baseball game is a random variable with the distribution x 0 1 2 p(x) 0.4 0.4 0.2 the team plays 2 games. the number of home runs scored in one game is independent of the number of home runs in the other game. let y be the total number of home runs. find e(y ) and var(y ).

E(Y) = 1.6 and Var(Y)=1.12

Step-by-step explanation:

Since we have given that

X       0        1       2

P(X)   0.4   0.4    0.2

Here, number of games = 2

So,

Since are independent variables.

so,

So, we get that

So, E[y]=2×0.8=1.6

and Var[y]=2×0.56=1.12

Hence, E(Y) = 1.6 and Var(Y)=1.12

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2