Let a pair of dice be thrown and the random v | vedclass

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

Question

(A) The sample space of the experiment consists of $36$ elementary events in the form of ordered pairs $(x_i, y_i)$,where $x_i, y_i \in \{1, 2, 3, 4,

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(A) The sample space of the experiment consists of $36$ elementary events in the form of ordered pairs $(x_i, y_i)$,where $x_i, y_i \in \{1, 2, 3, 4, 5, 6\}$.The random variable $X$,representing the sum of the numbers on the two dice,takes values $x_i \in \{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}$.The probability distribution of $X$ is given by:$X$$P(X)$$2$$1/36$$3$$2/36$$4$$3/36$$5$$4/36$$6$$5/36$$7$$6/36$$8$$5/36$$9$$4/36$$10$$3/36$$11$$2/36$$12$$1/36$The mean or expectation $E(X)$ is calculated as $\mu = \sum x_i p_i$:$E(X) = 2(\frac{1}{36}) + 3(\frac{2}{36}) + 4(\frac{3}{36}) + 5(\frac{4}{36}) + 6(\frac{5}{36}) + 7(\frac{6}{36}) + 8(\frac{5}{36}) + 9(\frac{4}{36}) + 10(\frac{3}{36}) + 11(\frac{2}{36}) + 12(\frac{1}{36})$$E(X) = \frac{2 + 6 + 12 + 20 + 30 + 42 + 40 + 36 + 30 + 22 + 12}{36}$$E(X) = \frac{252}{36} = 7$Thus,the mean of the sum of the numbers is $7$.

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

Let a pair of dice be thrown and the random variable $X$ be the sum of the numbers that appear on the two dice. Find the mean or expectation of $X$.

Similar Questions

Two numbers are selected at random (without replacement) from the first six positive integers. Let $X$ denote the larger of the two numbers obtained. Find $E(X)$.

Find the mean number of heads in three tosses of a fair coin.

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 $4$.

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

If $X$ is a Poisson variate satisfying the condition $3 P(X=2)=P(X=4)$,then find $P(X=6)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module