Let X be a random variable defining number of stud – Class 12 Business Mathematics Statistics | ConceptFirst

Question 22 of 41

Q.

Let X be a random variable defining number of students getting A grade. Find the expected value of X from the given table.

$X = x$	$0$	$1$	$2$	$3$
$P(X = x)$	$0.2$	$0.1$	$0.4$	$0.3$

Tamil Nadu DgeTamil Nadu HSC (DGE) Commerce Board 2022Subjective· 2mImportance★★★★★

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Apply $E(X)=\sum x\,P(X=x)$ to the given table; the answer is $1.8$ .

For a discrete random variable the mathematical expectation (mean) is

$E(X)=\sum x\,P(X=x).$

Using the table:

$E(X)=0(0.2)+1(0.1)+2(0.4)+3(0.3)$

$=0+0.1+0.8+0.9=1.8.$ …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2026Set MARCH1 markMCQ
$E(6x)$
(a) $0$
(b) $6\,E(x)$
(c) $36\,E(x)$
(d) $E(x)$
›Reveal solutionSolution

Expectation is linear, so $E(6x)=6E(x)$ .

A key property of mathematical expectation is that a constant factor pulls out of the expectation. For any constant $a$ ,

$E(aX) = a\,E(X).$

With $a=6$ :

$E(6X) = 6\,E(X).$

…

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CBSE 2024Set MARCH1 markMCQ
$E(X)=5$
(a) $3$
(b) $7$
(c) $5$
(d) $-2$
›Reveal solutionSolution

$E(X-Y)=E(X)-E(Y)=5-(-2)=7$ .

By the linearity of mathematical expectation,

…

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CBSE 2023Set MARCH1 markMCQ
$E[X-E(X)]$
(a) $0$
(b) $E(X)$
(c) $E(X)-X$
(d) $V(X)$
›Reveal solutionSolution

Expectation is linear and $E(X)$ is a constant, so the mean deviation $E[X-E(X)]=0$ .

Let $\mu=E(X)$ , which is a constant. Using linearity of expectation:

$E[X-E(X)]=E(X)-E\big(E(X)\big)=E(X)-E(X)=\mu-\mu=0.$ …

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CBSE 2023Set MARCH1 markMCQ
$p(x)=\dfrac{1}{10}$
(a) $1$
(b) Zero
(c) $-1$
(d) $\dfrac{6}{8}$
›Reveal solutionSolution

Mathematical expectation is $\sum x\,p(x)$ ; here $10\times\tfrac{1}{10}=1$ .

The expected value of a discrete random variable is

$E(X)=\sum x\,p(x).$

…

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