A box contains 6 pens,2 of which are defectiv | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) $x$ : number of defective pens. Two pens are taken from the box. Therefore,$x$ can take values $0, 1, 2$. $P(x=0) = \frac{{}^4C_2}{{}^6C_2} = \fra

Vedclass · Accepted Answer

$\frac{4}{3 \sqrt{5}}$

Vedclass · Answer

(D) $x$ : number of defective pens. Two pens are taken from the box. Therefore,$x$ can take values $0, 1, 2$. $P(x=0) = \frac{{}^4C_2}{{}^6C_2} = \frac{6}{15}$ $P(x=1) = \frac{{}^2C_1 	imes {}^4C_1}{{}^6C_2} = \frac{8}{15}$ $P(x=2) = \frac{{}^2C_2}{{}^6C_2} = \frac{1}{15}$   $x_i$ $P(x_i)$ $x_i P(x_i)$ $x_i^2 P(x_i)$   $0$ $\frac{6}{15}$ $0$ $0$   $1$ $\frac{8}{15}$ $\frac{8}{15}$ $\frac{8}{15}$   $2$ $\frac{1}{15}$ $\frac{2}{15}$ $\frac{4}{15}$   $E(x) = \sum x_i P(x_i) = 0 + \frac{8}{15} + \frac{2}{15} = \frac{10}{15} = \frac{2}{3}$ $E(x^2) = \sum x_i^2 P(x_i) = 0 + \frac{8}{15} + \frac{4}{15} = \frac{12}{15} = \frac{4}{5}$ $	ext{Variance}(x) = E(x^2) - [E(x)]^2 = \frac{4}{5} - (\frac{2}{3})^2 = \frac{4}{5} - \frac{4}{9} = \frac{36-20}{45} = \frac{16}{45}$ $	ext{Standard Deviation} = \sqrt{	ext{Variance}(x)} = \sqrt{\frac{16}{45}} = \frac{4}{3 \sqrt{5}}$

$X=x$	$1$	$2$	$3$	$4$
$P(X=x)$	$2k$	$4k$	$3k$	$k$

Outcome	Probability
$\omega_{1}$	$1/8$
$\omega_{2}$	$2/3$
$\omega_{3}$	$1/3$
$\omega_{4}$	$1/3$
$\omega_{5}$	$-1/4$
$\omega_{6}$	$-1/3$

$A$ box contains $6$ pens,$2$ of which are defective. Two pens are taken randomly from the box. If random variable $x$ represents the number of defective pens obtained,then the standard deviation of $x$ is:

Similar Questions

$A$ random variate $X$ takes the values $0, 1, 2, 3$ and its mean is $1.3$. If $P(X=3) = 2 P(X=1)$ and $P(X=2) = 0.3$,then $P(X=0)$ is equal to:

If the probability distribution of a random variable $X$ is as follows,then $k=$
$X=x$ $1$ $2$ $3$ $4$
$P(X=x)$ $2k$ $4k$ $3k$ $k$
(in $/10$)

The probability distribution of a random variable $X$ is given below. Then, the standard deviation of $X$ is
$X=x_i$ $2$ $3$ $5$ $7$ $12$
$P(X=x_i)$ $3k$ $k$ $k$ $2k$ $k$

Let a sample space be $S = \{\omega_{1}, \omega_{2}, \ldots, \omega_{6}\}$. Which of the following assignments of probabilities to each outcome is valid?

Outcome Probability

$\omega_{1}$ $1/8$

$\omega_{2}$ $2/3$

$\omega_{3}$ $1/3$

$\omega_{4}$ $1/3$

$\omega_{5}$ $-1/4$

$\omega_{6}$ $-1/3$

If a random variable $X$ denotes the number that appears on the upper face of a die when it is rolled,then $\frac{\text{Variance of } X}{\text{Mean of } X}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module