Question

A machine's time until failure is t=xy. x and y are independent random variables with Var(x)=Var(y)=10. Compute Var(t).

a. 20
b. 30
c. 40
d. 50

Answer 1

The variance of t, which represents the time until failure of a machine, is 130.

This correct answer is none of the above.

Step-by-step explanation:

The time until failure of a machine is given by the product of two independent random variables x and y, where Var(x) = Var(y) = 10.

To find the variance of t, we can use the formula Var(t) = Var(x)E(y)^2 + E(x)^2Var(y) + Var(x)Var(y).

Since x and y are independent, we have E(x*y) = E(x) * E(y), and Var(x*y) = E(x^2) * Var(y) + Var(x) * E(y^2).

Substituting the given values, we get Var(t) = 10 * E(y^2) + 10 * E(x^2) + 10 * 10 = 20 + 10 + 100 = 130.

This correct answer is none of the above.