# Statistics PDF and change of variable

1. Oct 8, 2011

### Larrytsai

If the probability density of X is given by

f(x) =

{2(1 − x) for 0 ≤ x ≤ 1
{0 otherwise

(a) Find the probability density function of Y1 = 2X − 1.

Is there a formula that Im missing from my notes to solve this problem?

2. Oct 8, 2011

### LCKurtz

Start by finding the cumulative distribution function of Y:

P(Y ≤ y) = P(2X-1 ≤ y) = P(X ≤ ?)

Figure that out for various y and use the fact that the density function is the derivative of the distribution function.

3. Oct 8, 2011

### Bacle

To add to what LC said:

If you know the distribution/density of a variable X, what can you say about

the density/distribution of f(X)?

4. Oct 8, 2011

### Larrytsai

LCKurtz:

so P(X≤ (Y+1/2))

Bacle:

that means we can say f(X) gives us the probability of X?

5. Oct 8, 2011

### LCKurtz

That isn't correct as you have written it. You need proper parentheses and, to be pedantic about it, a lower case y. Then use the density of X to calculate the probability.

6. Oct 8, 2011

### Bacle

7. Oct 15, 2011

### aliafi90

can anyone explain the steps towards the solution? i'm really confused here too,thank you