Question

A die is tossed thrice. A success is getting 1 or 6 on a toss. The mean and the variance of number of successes

• A. $\mu = 1 , \sigma ^ { 2 } = 2 / 3$
• B. $\mu = 2 / 3 , \sigma ^ { 2 } = 1$
• C. $\mu = 2 , \sigma ^ { 2 } = 2 / 3$
• D. None of these

Answer 1

Answer: (A)

$\mu = 1 , \sigma ^ { 2 } = 2 / 3$

Answer 2

For binomial distribution, mean$= n p$ and variance

$= n p q$

$n = 3$ $p = \frac { 2 } { 6 } = \frac { 1 } { 3 }$ $q = 1 - p = 1 - \frac { 1 } { 3 } = \frac { 2 } { 3 }$

So, mean $( \mu ) = 3 \times \frac { 1 } { 3 } = 1$

Variance $\left( \sigma ^ { 2 } \right) = 3 \times \frac { 1 } { 3 } \times \frac { 2 } { 3 } = \frac { 2 } { 3 }$.