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

  • $\begingroup$ 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? $\endgroup$ – Mild_Thornberry Dec 6 '19 at 0:09
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    $\begingroup$ I'm voting to close this question as off-topic because it should be on the math or stats sites $\endgroup$ – Slade Dec 6 '19 at 1:39
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    $\begingroup$ This is a problem in Order Statistics (not Finance). Do some research on "order statistics for the uniform distribution". $\endgroup$ – 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 $X_i$

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