If $X$ has a binomial distribution, $B (n, p)$ with parameters $n$ and $p$ such that $P (X = 2) = P (X = 3)$ , then $E (X)$ , the mean of variable $X$ , is :

3 - p

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\frac{p}{2}

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\frac{p}{3}

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2 - p

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Solution

The correct option is A $3 - p$
$P (x = n) =^{n} C_{x} (1 - P)^{n - x} P^{x}$
$^{n} C_{2} (a - P)^{n - 2} P_{2} =^{n} C_{3} (1 - P)^{n - 2} P^{3}$
$^{n} C_{2} = n_{3}^{C} \frac{P}{1 - P}$
$\frac{1}{(n - 2)} = \frac{P}{3 (1 - P)}$
$n P = 3 - P$
$E (x) = n P$
$E (x) = 3 - P$ .

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