Statistics Question 3

Question 3 - 29 January - Shift 1

There rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable $X$ denote the number of rotten apples. If $\mu$ and $\sigma^{2}$ represent mean and variance of $X$, respectively, then $10(\mu^{2}+\sigma^{2})$ is equal to

(1) 20

(2) 250

(3) 25

(4) 30

Show Answer

Answer: (1)

Solution:

Formula: Probability of occurrence of an event, Probability distribution

$x$ $P(x)$ $xP(x)$ $x^{2} P(x)$
0 $1 / 6$ 0 0
1 $1 / 2$ $1 / 2$ $1 / 2$
2 $3 / 10$ $6 / 10$ $12 / 10$
3 $1 / 30$ $1 / 10$ $9 / 30$

$\sum xP(x)=\frac{6}{2}=\mu$

$\sigma^{2}=\sum x^{2} P(x)-\mu^{2}$

$\sigma^{2}+\mu^{2}=0+\frac{1}{2}+\frac{12}{10}+\frac{9}{30}=2$

$10(\sigma^{2}+\mu^{2})=20$ (Ans.)