- #1
Kior
- 11
- 0
Here is a question about probability density. I am trying to work it out using a different method from the method on the textbook. But I get a different answer unfortunately. Can anyone help me out?
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
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