Question

Topic: Linear Combination Of Random Variables

Suppose X and Y are independent random variables with X ∼ N(1, 9) and Y ∼ N(2, 16). Find the probability that 2Y ≥ 1; find the probability that X − Y ≥ 0.

Answer 1

X and Y are independent random variables with

X ∼ N(1, 9) and

Y ∼ N(2, 16)

Part a

Using Normal table distribution

Part b

find the probability that X − Y ≥ 0.

X ∼ N(1, 9) and

Y ∼ N(2, 16)

According to question X and Y are independent

Then

X-Y ~ N(1-2,9+16)

W (say) = X-Y ~ N(-1,25)

Now

Using Normal table distribution