Originally Posted by

**Integrator020** Hello everyone! I solved (or rather, tried to) a couple of problems, and I was wondering if I attempted them correctly. Any feedback would be wonderful! Thank you in advance!

**1) Suppose the p.d.f. of X is **

**f(x) = 1/2x for 0 < x < 2**

**and 0 otherwise.**

**Determine the p.d.f. of Y = 3X + 2.**

My solution:

I found the inverse of Y = 3X + 2.

This came out to be (y-2)/3 = x.

Now, I substituted this value in for x in f(x).

This gave f(x) = (3/2)/(y-2).

Then, I found the derivative of (y-2)/3.

This turned out to be 1/3.

Multiplying (1/3) * (3/2)/(y-2) gave me (1/2)(y-2).

So if the above work is correct, the p.d.f. of Y = 3X + 2 is

(1/2)(y-2) for 2 < y < 8

and 0 otherwise.

**2) Suppose the p.d.f. of X is **

**f(x) = e^-x for x > 0,**

**and 0 for x less than or equal to 0.**

**Determine the p.d.f. of Y = X^(1/2)**

I found the inverse of Y = X^(1/2).

This turned out to be Y^2 = X.

Then, I subbed in y^2 for x in f(x).

This gave e^(-y^2).

Now, the derivative of y^2 is 2.

Multiplying gives 2*e^(-y^2) as the p.d.f., where y lies between negative infinity and positive infinity.