- #1

Kior

- 11

- 0

Question:

Let X be uniformly distributed random variable in the internal [ 0, 1]. Find the probability density of X^2?

My trial:

FY(y) = P(Y≤y) = P(X^2≤y) = P(X≤√y) = FX(√y) = ∫ (from 0 to √y) t dt = 0.5 y ⟹ 0.5 = fY(y).

This is actually inspired by http://math.stackexchange.com/questions/...

Solution on the textbook:

y = x^2

dy = 2x dx

h(y)dy = 1 dx

h(y) 2x dx = dx

h(y) = 0.5/x = 0.5/√y