In a Binomial distribution $B(n, p)$, if the mean and variance are 15 and 10 respectively, then the value of the parameter $n$ is
Show Hint
- $28$
- $16$
- $45$
- $25$
The Correct Option is C
Solution and Explanation
Mean $= np = 15$
Variance $= np(1 - p) = 10$
So, $15(1 - p) = 10 \Rightarrow 1 - p = \dfrac{2}{3} \Rightarrow p = \dfrac{1}{3}$
Now, $n = \dfrac{15}{p} = \dfrac{15}{1/3} = 45$
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