Given X sim B(n, p),if E(X) = 4 and operatorn | vedclass

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(D) For a binomial distribution $X \sim B(n, p)$,the mean is given by $E(X) = np$ and the variance is given by $\operatorname{Var}(X) = npq$,where $q

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$10$

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(D) For a binomial distribution $X \sim B(n, p)$,the mean is given by $E(X) = np$ and the variance is given by $\operatorname{Var}(X) = npq$,where $q = 1 - p$.Given $E(X) = np = 4$.Given $\operatorname{Var}(X) = npq = 2.4$.Substituting $np = 4$ into the variance equation: $4q = 2.4$.Solving for $q$: $q = \frac{2.4}{4} = 0.6 = \frac{3}{5}$.Since $p = 1 - q$,we have $p = 1 - 0.6 = 0.4 = \frac{2}{5}$.Now,substitute $p$ back into the mean equation: $n 	imes \frac{2}{5} = 4$.$n = 4 	imes \frac{5}{2} = 10$.Thus,the value of $n$ is $10$.

Given $X \sim B(n, p)$,if $E(X) = 4$ and $\operatorname{Var}(X) = 2.4$,then $n = $

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