(B) The expected value $E(X)$ of a random variable $X$ is given by the formula $E(X) = \sum p_i x_i$.Using the provided table:$E(X) = (0 \times 0.35)

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(B) The expected value $E(X)$ of a random variable $X$ is given by the formula $E(X) = \sum p_i x_i$.Using the provided table:$E(X) = (0 \times 0.35) + (500 \times 0.25) + (1000 \times 0.15) + (1500 \times 0.10) + (2000 \times 0.08) + (2500 \times 0.05) + (3000 \times 0.02)$Calculating each term:$E(X) = 0 + 125 + 150 + 150 + 160 + 125 + 60$Summing the values:$E(X) = 770$Thus,the expected value of the maintenance cost is Rs. $770$.

Class 12 Mathematics Probability Probability distribution

Easy

Rajesh has just bought a $VCR$ from Maharashtra Electronics and the shop offers an after-sales service contract for Rs. $1000$ for the next five years. Considering the experience of $VCR$ users,the following distribution of maintenance expenses for the next five years is formed:
Expenses $0$ $500$ $1000$ $1500$ $2000$ $2500$ $3000$
Probability $0.35$ $0.25$ $0.15$ $0.10$ $0.08$ $0.05$ $0.02$

The expected value of the maintenance cost is:

Expenses	$0$	$500$	$1000$	$1500$	$2000$	$2500$	$3000$
Probability	$0.35$	$0.25$	$0.15$	$0.10$	$0.08$	$0.05$	$0.02$

MHT CET 2021 All MHT CET

A
Rs. $800$
B
Rs. $770$
C
Rs. $700$
D
Rs. $900$

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Two cards are drawn simultaneously (or successively without replacement) from a well-shuffled pack of $52$ cards. Find the mean,variance,and standard deviation of the number of kings.

Difficult

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$A$ coin is tossed three times. If $X$ denotes the absolute difference between the number of heads and the number of tails,then $P(X=1) = $

MediumMHT CET 2018

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Two balls are drawn at random from a bag containing $5$ black balls and $3$ white balls. If the random variable $X$ denotes the number of white balls drawn, then the mean of $X$ is

MediumTS EAMCET 2022

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If a fair coin is tossed $5$ times,the probability that heads does not occur two or more times in a row is

DifficultKVPY 2017

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If $m$ and $\sigma^2$ are the mean and variance of the random variable $X$,whose distribution is given by:
$X=x$ $0$ $1$ $2$ $3$
$P(X=x)$ $\frac{1}{3}$ $\frac{1}{2}$ $0$ $\frac{1}{6}$

Then:

$X=x$	$0$	$1$	$2$	$3$
$P(X=x)$	$\frac{1}{3}$	$\frac{1}{2}$	$0$	$\frac{1}{6}$

MediumAP EAMCET 2009

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Two cards are drawn simultaneously (or successively without replacement) from a well-shuffled pack of $52$ cards. Find the mean,variance,and standard deviation of the number of kings.

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If $m$ and $\sigma^2$ are the mean and variance of the random variable $X$,whose distribution is given by:
$X=x$ $0$ $1$ $2$ $3$
$P(X=x)$ $\frac{1}{3}$ $\frac{1}{2}$ $0$ $\frac{1}{6}$

Then: