X has B(n,p) with mean 4 and variance 43.

Question

$X$ has $B(n,p)$ with mean 4 and variance $\dfrac43$. Find $54P(X\le2)$.

Accepted Answer

$np=4$, $npq=\dfrac43\Rightarrow q=\dfrac13,p=\dfrac23,n=6$.

$$P(X\le2) = \frac{1}{3^6}[1+12+60]=\frac{73}{3^6}$$

$$54P(X\le2) = \frac{73\times54}{729}=\frac{146}{27}$$

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