Question

Mean and variance of a binomial distribution are 4 and (8/3) respectively. The value of p will be​

Answer 1

Answer:

Mean and variance of a binomial distribution are 4 and (8/3) respectively. The value of n will be​ 12.

Explanation:

Step 1: In probability theory and statistics, the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success or failure, is known as the binomial distribution with parameters n and p.

Step 2: Mean =n p=4

Variance =n p(1-p)=8 / 3

$n p q=12 \times 1 / 3 \times 2 / 3=8 / 3$

$\begin{aligned}& E(X)=n p=4 \\& V(X)=n p q=\frac{\overline{8}}{3} \\& q=\frac{2}{3}, p=\frac{1}{3} \\& \therefore n=12\end{aligned}$

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