Question

Let \(X\) be a discrete random variable, \(\mu\) be its mean, and \(P(X=x)\) be the probability function. The variance of \(X\) is

• A. \(\displaystyle \sum x^2P(X=x)-\sum x(P(X=x))^2\)
• B. \(\displaystyle \sum (x-\mu)P(X=x)\)
• C. \(\displaystyle \sum x^2P(X=x)-\mu^2\)
• D. \(\displaystyle \sum x^2P(X=x)-\left(\sum x\right)^2\)

Hint:

Remember the two most important formulas for a discrete random variable: \[ E(X)=\sum xP(X=x), \] \[ \boxed{\operatorname{Var}(X)=E(X^2)-[E(X)]^2.} \] These formulas are frequently used in probability and statistics.

Answer 1

The Correct Option is C