Second moment from a given mean and variance

Question

A random variable $X$ has mean $3$ and variance $25$ . What is $\mathbb{E}[X^2]$ ?

Short answer

$34$ . Rearranging $\text{Var}(X)=\mathbb{E}[X^2]-(\mathbb{E}[X])^2$ gives $\mathbb{E}[X^2]=25+9=34$ .

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Lessons behind this question

Expectation, Mean, and Variance
Conditional Probability, Total Probability, and Bayes' Rule
Worked Examples — Probability Trees, Monty Hall, and Bayesian Updating

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