Question

\(Y_1~N(5,1)\)
\(Y_2~N(4,3)\)
\(Y_1,Y_2\) are independent.
find \(P(Y_1>Y_2)\)
I got 0.5987 but the answer from the book is 0.6915. Please, help

Answer 1

Let \(U = Y_1-Y_2\)~ N(1,4)
Hence P(U>0) = 0.5987 (from calculator)

Answer 2

@Zarkon , please.

Answer 3

your calculator probably uses the standard deviation as an input and not the variance

your standard deviation is 2...use that number in your calculator

Answer 4

the notation is \[X\sim N(\mu,\sigma^2)\]

Answer 5

I got you.
Just make the information clear. So standard deviation =\(\sqrt {variance}\), right, that is where 2 come from, right?

Answer 6

yes

Answer 7

Thanks a lot. I am glad to have you as my Mentor. :)