Suppose there is a discrete r.v.s X, all we know is: E(X) = 10 and VAR(X) = 2500
Any general way to find PMF of X?
Thanks.
2026-03-27 21:35:39.1774647339
ls it possible to construct discrete r.v.s given expectation and variance?
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The mean and variance do not completely determine the pmf. There are infinitely many pmfs's with mean $10$ and variance $2500$. To find on example of such a pmf you take a random variable taking two values $a$ and $b$ with probability $\frac 1 2$ each and solve for $a$ and $b$ from the given conditions. This gives $P(X=60)=P(X=-40)=\frac 1 2$.