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.)
