# Suppose that X is a random variable uniform in (0, 1), and define $M = 2 \max\{X, 1− X\} − 1$. Determine the distribution function of M.

So far I got to transforming the variable and splitting it because of max into
for x>0.5: (1-x)/2
for x< 0.5: (x-1)/2

Now I should plug it into the CDF for X, but I am unsure what the CDF is with the boundaries given. Any help much appreciated, hope the 5 bucks are enough.

Can anyone explain shortly how to get there and solve the question?

Answers can be viewed only if
1. The questioner was satisfied and accepted the answer, or
2. The answer was disputed, but the judge evaluated it as 100% correct.
• is P(X<=t) supposed to be t/2 in the equality you called the most difficult one? Otherwise i think im following

• sorry this i understand now. but the very last equality is the last thing that confuses me. How does P(1-t/2

• also i think you forgot the -1 at the end of M

• I did forget the -1 at the end. Let me fix it!

• I fixed the missing -1 and a smally typo!

• thanks a lot! youre saving my exam tmrw