If a discrete random variable X takes values | vedclass

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

Question

(B) Given that $P(X=x) = k(x+1) 5^{-x}$ for $x = 0, 1, 2, 3, \ldots$. Since the sum of all probabilities must be $1$,we have $\sum_{x=0}^{\infty} P(X=

Vedclass · Accepted Answer

$\frac{16}{25}$

Vedclass · Answer

(B) Given that $P(X=x) = k(x+1) 5^{-x}$ for $x = 0, 1, 2, 3, \ldots$. Since the sum of all probabilities must be $1$,we have $\sum_{x=0}^{\infty} P(X=x) = 1$. $k \sum_{x=0}^{\infty} (x+1) (\frac{1}{5})^x = 1$. This is an arithmetico-geometric series of the form $\sum_{x=0}^{\infty} (x+1) r^x$ where $r = \frac{1}{5}$. The sum of this series is given by $\frac{1}{(1-r)^2}$. So,$k 	imes \frac{1}{(1 - \frac{1}{5})^2} = 1$. $k 	imes \frac{1}{(\frac{4}{5})^2} = 1$. $k 	imes \frac{25}{16} = 1$,which gives $k = \frac{16}{25}$. Now,$P(X=0) = k(0+1) 5^{-0} = k(1)(1) = k$. Therefore,$P(X=0) = \frac{16}{25}$.

$x$	$1$	$2$	$3$	$4$	$5$	$6$
$P(X=x)$	$a$	$a$	$a$	$b$	$b$	$0.3$

$Z$	$3$	$2$	$1$	$0$	$-1$
$P(Z)$	$0.3$	$0.2$	$0.4$	$0.1$	$0.05$

If a discrete random variable $X$ takes values $0, 1, 2, 3, \ldots$ with probability $P(X=x) = k(x+1) 5^{-x}$,where $k$ is a constant,then $P(X=0)$ is

Similar Questions

The probability distribution of a random variable $X$ is given below:
$x$ $1$ $2$ $3$ $4$ $5$ $6$
$P(X=x)$ $a$ $a$ $a$ $b$ $b$ $0.3$

If the mean of $X$ is $4.2$,then $a$ and $b$ are respectively equal to:

If three fair coins are tossed,then the variance of the number of heads obtained is

If $P(X=x)=k\left(\frac{3}{8}\right)^{X}, x=1,2,3, \ldots$ is the probability distribution function of a discrete random variable $X$,then $k=$

The range of a random variable $X$ is $\{0, 1, 2\}$. If $P(X = 0) = 3c^3$,$P(X = 1) = 4c - 10c^2$,and $P(X = 2) = 5c - 1$,then find $P(0 < X \le 2)$.

State which of the following is not the probability distribution of a random variable. Give reasons for your answer.

$Z$ $3$ $2$ $1$ $0$ $-1$

$P(Z)$ $0.3$ $0.2$ $0.4$ $0.1$ $0.05$

Vedclass Test Series

Exam Paper Generator

Online Exam Module