Distribution Function for 1/2X and (lambda)X

[JosephLee]

Homework Statement

Let X have an Exp(1/2) distribution. Determine the distribution function of 1/2X. What kind of distribution does 1/2X have?

The Attempt at a Solution

I can't seem to do this quite properly. I thought of doing the integral from x to -inf of 1/2X dx but that doesn't seem right. I know what a exponential distribution is but nothing else from there.

Is it just something like X = exp(1/2) therefore 1/2X = exp(1/4) or something along those lines?


thanks for the help in advance.

 

[LCKurtz]

Does 1/2X mean (1/2)X or 1/(2X)? I guess I will assume the former. Parentheses do serve a purpose you know.

If Y = (1/2)X then P(Y ≤ x) = P((1/2)X ≤ x) = P(X ≤ 2x)

Does that help you?

 

[JosephLee]

im sorry, its (1/2)X.

Does this change anything?

also along those same lines, there's another part to the question which is exactly the same as above but its:

let X have a exp(lambda) distribution...determine the distribution function of (lambda)X and what kind of distribution does this have?

 

[LCKurtz]

"Does this change anything?"

No, I assumed that.

"also along those same lines, there's another part to the question which is exactly the same as above but its:

let X have a exp(lambda) distribution...determine the distribution function of (lambda)X and what kind of distribution does this have?"

Did you understand my first reply. That should help.