If m and {sigma ^2} are the mean and variance | vedclass

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

Question

(C) The mean $m$ is calculated as $E(X) = \sum x_i P(x_i)$.$m = (0 	imes \frac{1}{3}) + (1 	imes \frac{1}{2}) + (2 	imes 0) + (3 	imes \frac{1}{6}

Vedclass · Accepted Answer

$m = {\sigma ^2} = 1$

Vedclass · Answer

(C) The mean $m$ is calculated as $E(X) = \sum x_i P(x_i)$.$m = (0 	imes \frac{1}{3}) + (1 	imes \frac{1}{2}) + (2 	imes 0) + (3 	imes \frac{1}{6}) + (4 	imes 0) = 0 + \frac{1}{2} + 0 + \frac{1}{2} + 0 = 1$.The variance ${\sigma ^2}$ is calculated as $E(X^2) - [E(X)]^2$.First,calculate $E(X^2) = \sum x_i^2 P(x_i)$.$E(X^2) = (0^2 	imes \frac{1}{3}) + (1^2 	imes \frac{1}{2}) + (2^2 	imes 0) + (3^2 	imes \frac{1}{6}) + (4^2 	imes 0) = 0 + \frac{1}{2} + 0 + \frac{9}{6} + 0 = \frac{1}{2} + \frac{3}{2} = 2$.Now,${\sigma ^2} = E(X^2) - m^2 = 2 - (1)^2 = 2 - 1 = 1$.Thus,$m = 1$ and ${\sigma ^2} = 1$.

$X=x$	$0$	$1$	$2$	$3$	$4$
$P(X=x)$	$\frac{1}{3}$	$\frac{1}{2}$	$0$	$\frac{1}{6}$	$0$

$X = x$	$0$	$1$	$2$	$3$
$P(X = x)$	$\frac{1}{10}$	$\frac{2}{10}$	$\frac{3}{10}$	$\frac{4}{10}$

$X = x$	$1$	$2$	$3$	$4$
$P(X = x)$	$1/10$	$2/10$	$3/10$	$4/10$

If $m$ and ${\sigma ^2}$ are the mean and variance of a random variable $X$,whose distribution is given by:
$X=x$ $0$ $1$ $2$ $3$ $4$
$P(X=x)$ $\frac{1}{3}$ $\frac{1}{2}$ $0$ $\frac{1}{6}$ $0$

,then:

Similar Questions

The p.d.f. of a continuous random variable $X$ is $f(x)=\begin{cases} \frac{x^2}{18} & \text{if } -3 < x < 3 \\ 0 & \text{otherwise} \end{cases}$. Then $P[|X| < 2]=$

If a random variable $X$ has a probability mass function $P(x) = \begin{cases} kx^2, & \text{for } x = 1, 2, 3, 4 \\ 0, & \text{otherwise} \end{cases}$, then the mean of $X$ is ...

The probability distribution of a random variable $X$ is given below.

$X = x$ $0$ $1$ $2$ $3$

$P(X = x)$ $\frac{1}{10}$ $\frac{2}{10}$ $\frac{3}{10}$ $\frac{4}{10}$

Then the variance of $X$ is

The probability distribution of a random variable $X$ is given by:
$X = x$ $1$ $2$ $3$ $4$
$P(X = x)$ $1/10$ $2/10$ $3/10$ $4/10$

Then the cumulative distribution function (c.d.f.) $F(x)$ of $X$ is given by:

$A$ 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:

Vedclass Test Series

Exam Paper Generator

Online Exam Module

If $m$ and ${\sigma ^2}$ are the mean and variance of a random variable $X$,whose distribution is given by:$X=x$$0$$1$$2$$3$$4$$P(X=x)$$\frac{1}{3}$$\frac{1}{2}$$0$$\frac{1}{6}$$0$,then: