Three fair coins with faces numbered 1 and 0 | vedclass

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

Question

(B) Let $X$ be the random variable representing the sum of the numbers on the uppermost faces. The possible values of $X$ are $0, 1, 2, 3$. Since ther

Vedclass · Accepted Answer

$0.75$

Vedclass · Answer

(B) Let $X$ be the random variable representing the sum of the numbers on the uppermost faces. The possible values of $X$ are $0, 1, 2, 3$. Since there are $3$ coins,the total number of outcomes is $2^3 = 8$. The probability distribution is: $P(X=0) = \frac{1}{8}$ $P(X=1) = \frac{3}{8}$ $P(X=2) = \frac{3}{8}$ $P(X=3) = \frac{1}{8}$ $E(X) = \sum x_i p_i = 0 	imes \frac{1}{8} + 1 	imes \frac{3}{8} + 2 	imes \frac{3}{8} + 3 	imes \frac{1}{8} = \frac{0+3+6+3}{8} = \frac{12}{8} = 1.5$. $E(X^2) = \sum x_i^2 p_i = 0^2 	imes \frac{1}{8} + 1^2 	imes \frac{3}{8} + 2^2 	imes \frac{3}{8} + 3^2 	imes \frac{1}{8} = \frac{0+3+12+9}{8} = \frac{24}{8} = 3$. $Variance(X) = E(X^2) - [E(X)]^2 = 3 - (1.5)^2 = 3 - 2.25 = 0.75$.

$X = x$	$-2$	$-1$	$0$	$1$	$2$	$3$
$P(X = x)$	$\frac{1}{10}$	$k$	$\frac{1}{5}$	$2k$	$\frac{3}{10}$	$k$

Three fair coins with faces numbered $1$ and $0$ are tossed simultaneously. The variance $(X)$ of the probability distribution of random variable $X$,where $X$ is the sum of numbers on the uppermost faces,is

Similar Questions

Suppose $X$ has the following probability mass function $P(X=0)=0.2, P(X=1)=0.5, P(X=2)=0.3$. What is $E[X^2]$?

If $X$ is a Poisson variate such that $2 P(X=1)=5 P(X=5)+2 P(X=3)$,then the standard deviation of $X$ is

If a random variable $X$ has p.d.f. $f(x) = \begin{cases} \frac{ax^2}{2} + bx & , \text{if } 1 \leqslant x \leqslant 3 \\ 0 & , \text{otherwise} \end{cases}$ and $f(2) = 2$,then the values of $a$ and $b$ are,respectively

The distribution of a random variable $X$ is given below. The value of $k$ is:
$X = x$ $-2$ $-1$ $0$ $1$ $2$ $3$
$P(X = x)$ $\frac{1}{10}$ $k$ $\frac{1}{5}$ $2k$ $\frac{3}{10}$ $k$

$A$ discrete random variable $X$ takes values $10, 20, 30,$ and $40$,with probabilities $0.3, 0.3, 0.2,$ and $0.2$ respectively. Then the expected value of $X$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module