The variable X has pdf $$f(x) = \frac18(6 - x)$$ for $$2 ≤ x ≤ 6$$
A sample of two values of X is taken. Denoting the lesser of the two values by Y, use the cdf of X to write down the cdf of Y. Hence obtain the pdf and mean of Y . Show that its median is approximately 2.64. (The median is the point m for which P(Y ≤ m) = 0.5.)
This is an exercise of Probability theory. It has been bothering me for a long time. Really thank you for helping me.
I am stuck in the first step:using the cdf of X to write down the cdf of Y.
I tried the Inverse function of cumulative distribution function, but it didn't seem to help.