If a discrete random variable X has the proba | vedclass

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

Question

(A) For a probability distribution,the sum of all probabilities must be $1$.Therefore,$k + 3k + 3k + k = 1$,which implies $8k = 1$,so $k = \frac{1}{8}

Vedclass · Accepted Answer

$\frac{3}{4}$

Vedclass · Answer

(A) For a probability distribution,the sum of all probabilities must be $1$.Therefore,$k + 3k + 3k + k = 1$,which implies $8k = 1$,so $k = \frac{1}{8}$.The mean $E(X) = \sum x_i P(x_i) = (0 	imes \frac{1}{8}) + (1 	imes \frac{3}{8}) + (2 	imes \frac{3}{8}) + (3 	imes \frac{1}{8}) = 0 + \frac{3}{8} + \frac{6}{8} + \frac{3}{8} = \frac{12}{8} = \frac{3}{2}$.The expected value of the square,$E(X^2) = \sum x_i^2 P(x_i) = (0^2 	imes \frac{1}{8}) + (1^2 	imes \frac{3}{8}) + (2^2 	imes \frac{3}{8}) + (3^2 	imes \frac{1}{8}) = 0 + \frac{3}{8} + \frac{12}{8} + \frac{9}{8} = \frac{24}{8} = 3$.The variance $Var(X) = E(X^2) - [E(X)]^2$.$Var(X) = 3 - (\frac{3}{2})^2 = 3 - \frac{9}{4} = \frac{12 - 9}{4} = \frac{3}{4}$.

$X = x$	$0$	$1$	$2$	$3$
$P(X = x)$	$k$	$3k$	$3k$	$k$

$X=x$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P(X=x)$	$0$	$k$	$2k$	$2k$	$3k$	$k^2$	$2k^2$	$7k^2+k$

$X$	$1$	$2$	$3$	$4$	$5$
$P(X)$	$K$	$2K$	$2K$	$3K$	$K$

If a discrete random variable $X$ has the probability distribution as follows:
$X = x$ $0$ $1$ $2$ $3$
$P(X = x)$ $k$ $3k$ $3k$ $k$

Then $Var(X) = $

Similar Questions

For a Poisson variate $X$,if $P(X=2)=3 P(X=3)$,then the mean of $X$ is:

If a random variable $X$ has the following probability distribution of $X$:

$X=x$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$

$P(X=x)$ $0$ $k$ $2k$ $2k$ $3k$ $k^2$ $2k^2$ $7k^2+k$

Then $P(X \geqslant 6) = $

The probability distribution of random variable $X$ is given by:

$X$ $1$ $2$ $3$ $4$ $5$

$P(X)$ $K$ $2K$ $2K$ $3K$ $K$

Let $p=P(1 < X < 4 \mid X < 3)$. If $5p = \lambda K$,then $\lambda$ is equal to .... .

If the probability that the random variable $X$ takes values $x$ is given by $P(X = x) = k(x + 1)3^{-x}$ for $x = 0, 1, 2, 3, \ldots$,where $k$ is a constant,then $P(X \geq 2)$ is equal to

Find the probability distribution of the number of successes in two tosses of a die,where a success is defined as a number greater than $4$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module

If a discrete random variable $X$ has the probability distribution as follows:$X = x$$0$$1$$2$$3$$P(X = x)$$k$$3k$$3k$$k$Then $Var(X) = $