Question
If $X$ is $b(n, p)$, show that$$E\left(\frac{X}{n}\right)=p \quad \text { and } \quad E\left[\left(\frac{X}{n}-p\right)^{2}\right]=\frac{p(1-p)}{n}$$
Step 1
We know that the expected value of a random variable is given by $E(X) = np$. So, we can write: $$ E\left(\frac{X}{n}\right)=\frac{1}{n}E(X) $$ Show more…
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