# How to derive the CDF and the probability density function [closed]

Is there something missing in this question i dont seem to understand, can anyone help explaining what is required?

• Smells like homework... but intuition makes me wanna guess beta? Bounded by [0, 1], more likely to be <.5, can be estimated using bi-variate case, where evaluating the CDFs is a binomial. Isn’t there a math exchange for these questions? – Mild_Thornberry Dec 6 '19 at 0:09
• I'm voting to close this question as off-topic because it should be on the math or stats sites – Slade Dec 6 '19 at 1:39
• This is a problem in Order Statistics (not Finance). Do some research on "order statistics for the uniform distribution". – Alex C Dec 6 '19 at 2:25

During the calculation of the distribution function of $$M$$, that is $$P(M \leq m)$$, there is an independency assumption being used. That is the condition you are missing, it seems like it was forgotten.

$$P(M \geq m) = P(X_1 \geq m, X_2 \geq m, ... X_n \geq m) =$$ (missing the independency condition here)

$$P(X_1 \geq m)P(X_2 \geq m)...P(X_n \geq m)= (1-m)^n$$

So $$P(M \leq m) = 1-(1-m)^n$$, as usual.

Without the independency condition you cannot proceed further in the calculation, unless you know more about the joint distribution of the $$X_i$$