# 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?

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• Kilian Schulz

is P(X<=t) supposed to be t/2 in the equality you called the most difficult one? Otherwise i think im following

• Kilian Schulz

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

• Kilian Schulz

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

• Mathe

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

• Mathe

I fixed the missing -1 and a smally typo!

• Kilian Schulz

thanks a lot! youre saving my exam tmrw