Assume X and Y are random variables with both have mean 3 and variance 2. Calculate E left square bracket X squared plus 4 Y minus 5 right square bracket. (Hint: Think how to calculateE left square bracket X squared right square bracket given the mean and the variance).

E[X² + 4Y - 5] = 18

Step-by-step explanation:

Mean = E(X) = 3

E(Y) = 3

Variance = Var(X) = 2

Var(Y) = 2

Calculate E[X² + 4Y - 5]

E[X² + 4Y - 5] = E(X²) + 4E(Y) - E(5)

But Var(X) = E(X²) - [E(X)]²

E(X²) = Var(X) + [E(X)]² = 2 + 3² = 2 + 9 = 11

E(5) = 5

E[X² + 4Y - 5] = E(X²) + 4E(Y) - E(5) = 11 + 4(3) - 5 = 11 + 12 - 5 = 18

Hope this Helps!!!

+25 = x

step-by-step explanation:

here x is the hypotenuse of a right triangle whose legs are 7 and 24.   by the pythagorean theorem, 7² + 24² must equal x²:

x² = 49 + 576 = 625.   thus, x = +√625 = +25 = x

answer: expected value of x = 1.0

step-by-step explanation:

p(x=0) = 0.25

p(x=1) = 0.50

p(x=2) = 0.25

expected value for x = 0×0.25 + 1×0.5 + 2×0.25 = 1.0