Hello All,

I've found this forum to be a lot of help. The answers provided to my last question were helpful and I'm hoping I can get similar help for this question.

Y has the standard normal distribution.

1. Determine the distribution function of |Y|, the absolute value of Y.

2. Determine the probability density function of |Y|

3. Find P(|Y|>1.70).

For part 1, I did this:

P(|Y|) ≤ x)= P(−x ≤ Y≤ x) =ϕ(x) −ϕ(-x)

=ϕ(x) -(1 −ϕ(x) ) = 2ϕ(x) − 1 .

Does that look correct?

For 2, this is my work,

f(x)=dP(|Y|) ≤ x)= 2ϕ'(x)

dx

Which is equal to 2*(1/√2π)*e^(-x^2/2)

Is my work right for this?

I'm not sure about how I would go about doing 3, so all tips are appreciated. Thanks.