Let the random variable X represent the length of the side of a square. It has a uniform distribution over the interval (0, 5).
What is the cumulative distribution function for the area of the square, Y?
F(x) = 0.2x (the cdf of the side).
The Attempt at a Solution
So I tried simply squaring F(x), giving 0.04x^2, which is incorrect since F(25) = 25 instead of 1. Also, it wouldn't make sense for the probability of the largest areas to have the highest probability, since:
P(4.9 < X < 5.0) = 0.02
Therefore P(4.9^2 < X < 5.0^2) = 0.02
But going by 0.04x^2 we get 0.08 or something.
Also, I couldn't find anything like this in my textbook (I'm a high school student), is there any good website to line this stuff from?
Thanks in advance.