# Cumulative Distribution Function problems

Let $a$ and $b$ be two positive integers. Let also $X$ be a discrete random variable varying in

$X(\Omega)=\{1, 2, \ldots, ab\}$ such that for every $x∈X(\Omega),P[X = x]=1/a - 1/b$.

a) What conditions should $a$ and $b$ satisfy?

b) Determine the cumulative distribution function $F$ of $X$. Compute $u$ such that $F(u)=1/2$.

c) Determine $E(X)$. Find the values of $a$ and $b$ such that $E(X) = 7/2$.

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Be careful! Please read our FAQ and the wiki for the Homework tag and note that questions from textbooks, like this one, are welcome provided you indicate what research you have done, what progress you have made, and specifically where you need help. Without that additional information, such questions will be closed automatically. To would-be respondents: please note that guidance is welcome, but detailed solutions are usually not. –  whuber Nov 9 '11 at 18:39
a) $P[X=x]=1/a−1/b$ and any probability is always $0≤P≤1$ so $0≤b-a≤ab$ –  Majed Hijazi Nov 9 '11 at 22:17
b) $F(X)=P(X≤x)=∑P(X=x)=1$. $F(u)=1/2=P(U≤u)$ and can't figure out how to continue.. –  Majed Hijazi Nov 9 '11 at 22:27
c) As i know $E(X)=∑XP(X)=∑xP(X=x)$ and also I can't figure out how to make this equality in terms of $a$ and $b$ only. –  Majed Hijazi Nov 9 '11 at 22:31