Question

4.72

Find some variances.

Suppose that X is a random variable with mean 30 and standard deviation 4. Also suppose that Y is a random variable with mean 50 and standard deviation 8. Find the VARIANCE of the random variable Z for each of the following cases. (HINT: remember the rules for linear transformation of variances.)

a) Z = 35 - 10 X Blank 1

b) Z = 12 X - 5 Blank 2

c) Z = X + Y Blank 3

d) Z = X - Y Blank 4

e) Z = -2 X + 2 Y Blank 5

Answer 1

Formula 1:

Formula 2:

(a)

Substituting Var(X) = 4, a = - 10 and b = 35 in Formula 1, we get:

So,

Answer is:

400

(b)

Substituting Var(X) = 4, a = 12 and b = - 5 in Formula 1, we get:

So,

Answer is:

576

(c)

Substituting Var(X) = 4, Var(Y) = 8, a = 1 and b = 1 in Formula 2, we get:

So,

Answer is:

12

(d)

Substituting Var(X) = 4, Var(Y) = 8, a = 1 and b = -1 in Formula 2, we get:

So,

Answer is:

12

(e)

Substituting Var(X) = 4, Var(Y) = 8, a = - 2 and b = 2 in Formula 2, we get:

So,

Answer is:

48