Two dice are rolled. If a random variable X i | vedclass

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

Question

(D) When two dice are rolled,the total number of outcomes is $6 	imes 6 = 36$. Let $X$ be the absolute difference of the numbers on the two dice. The

Vedclass · Accepted Answer

$\frac{35}{18}$

Vedclass · Answer

(D) When two dice are rolled,the total number of outcomes is $6 	imes 6 = 36$. Let $X$ be the absolute difference of the numbers on the two dice. The possible values of $X$ are $0, 1, 2, 3, 4, 5$. The probability distribution is as follows:| $X$ | $P(X)$ | $P_i X_i$ ||---|---|---|| $0$ | $6/36$ | $0$ || $1$ | $10/36$ | $10/36$ || $2$ | $8/36$ | $16/36$ || $3$ | $6/36$ | $18/36$ || $4$ | $4/36$ | $16/36$ || $5$ | $2/36$ | $10/36$ |The mean $\mu$ is given by $\sum P_i X_i$:$\mu = 0 + \frac{10}{36} + \frac{16}{36} + \frac{18}{36} + \frac{16}{36} + \frac{10}{36}$$\mu = \frac{10 + 16 + 18 + 16 + 10}{36} = \frac{70}{36} = \frac{35}{18}$.

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

Two dice are rolled. If a random variable $X$ is defined as the absolute difference of the two numbers that appear on them,then the mean of $X$ is

Similar Questions

$A$ 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

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

An urn contains $3$ black and $5$ red balls. If $3$ balls are drawn at random from the urn,the mean of the probability distribution of the number of red balls drawn is

The p.d.f. of a continuous random variable $X$ is given by $f(x) = \frac{x+2}{18}$ for $-2 < x < 4$ and $f(x) = 0$ otherwise. Then $P[|x| < 1] = $

If $X$ is a random variable with probability distribution $P(X=k) = \frac{(k+1)c}{2^k}$ for $k = 0, 1, 2, \ldots$,then $P(X \geq 3) = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module