If EX5 and VarX4 then E42X2 and Var35X SolutionAs varx Ex2

If E[X]=5 and Var(X)=4, then
E[(4+2X)2]=
and
Var(3+5X)= .

Solution

As

var(x) = E(x^2) - E(x)^2 = 4

Then

E(x^2) - 5^2 = 4

E(x^2) = 29

Now,

E[(4+2x)^2] = E(16 + 16x + 4x^2)

= 16 + 16E(x) + 4E(x^2)

= 16 + 16*5 + 4*29

= 212 [ANSWER]

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Var(3 + 5x) = 5^2 var(x) =25*4 = 100 [ANSWER]