# Thread: Standard Normal Distrbution question

1. ## Standard Normal Distrbution question

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)= d
P(|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.

2. This is tough to type with an I(dot) pad, but the prob of abs y greater than 1.7 is twice that y is greater than 1.7

3. Originally Posted by hwill205
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 [FONT=verdana, geneva, helvetica][SIZE=2][COLOR=#000000]|Y|, the absolute value of Y.
$F_{|Y|}(u)=Pr(|Y|0 \mbox{ and } 0 \mbox{ otherwise }$

Now write the right most probability in terms of the cumulative standard normal. Which is what you did, so yes.

CB

4. Originally Posted by hwill205
2. Determine the probability density function of [/COLOR][/SIZE][/FONT][FONT=verdana, geneva, helvetica][SIZE=2][COLOR=#000000]|Y|
Differentiate the cumulative distribution you get in part (1). Again this is what you did so yes.

CB