The expected value of X for the following p.m.f. | X | –2 | –1 | 0 | 1 | 2 | |---|---|---|---|---|---| | P (X) | 0.3 | 0.3 | 0.1 | 0.05 | 0.25 | (A) 0.85 (B) – 0.35 (C) 0.15 (D) – 0.15

The expected value of X for the following p.m.f. | – Class 12 Mathematics

Miscellaneous 7 (I) · Q46

The expected value of X for the following p.m.f.

X	–2	–1	0	1	2
P (X)	0.3	0.3	0.1	0.05	0.25

(A) 0.85

(B) – 0.35

(D) – 0.15

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$E(X)=(-2)(0.3)+(-1)(0.3)+0(0.1)+1(0.05)+2(0.25)=-0.6-0.3+0+0.05+0.5=- …

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CBSE 2023Set ANNUAL2 marksMCQ
$P(X=x) = {}^4C_x\left(\dfrac{5}{9}\right)^x \times \left(\dfrac{4}{9}\right)^{4-x}$
(a) $\dfrac{20}{9}$
(b) $\dfrac{9}{20}$
(c) $\dfrac{12}{9}$
(d) $\dfrac{9}{25}$
›Reveal solutionSolution

This is a Binomial $(4,\frac59)$ p.m.f.; $E(X)=np$ .

The given p.m.f. $P(X=x)={}^4C_x\left(\frac59\right)^x\left(\frac49\right)^{4-x}$ is a Binomial $(n=4,p=\frac59)$ distribution …

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CBSE 2023Set ANNUAL2 marks
$Q. Find the mean of number randomly selected from 1 to 15.$
›Reveal solutionSolution

Mean of a discrete uniform distribution on $\{1,\dots,15\}$ is $\dfrac{1+15}{2}$ .

…

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CBSE 2022Set ANNUAL2 marksMCQ
$P(x) = \dfrac{c}{x^3}$
(a) $\dfrac{216}{251}$
(b) $\dfrac{294}{251}$
(c) $\dfrac{297}{294}$
(d) $\dfrac{294}{297}$
›Reveal solutionSolution

First find $c$ from $\sum P(x)=1$ , then compute $E(X)=\sum xP(x)$ .

$\sum_{x=1}^3 P(x)=1$ : $\ c\left(1+\dfrac18+\dfrac1{27}\right)=1$

$1+\dfrac18+\dfrac1{27} = \dfrac{216+27+8}{216} = \dfrac{251}{216} \implies c=\dfrac{216}{251}$

…

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CBSE 2020Set ANNUAL2 marks
$Q. Find expected value of the random variable X whose probability mass function is: X = x: 1, 2, 3; P(X = x): 1/5, 2/5, 2/5.$
›Reveal solutionSolution

$E(X) = \sum x_i P(x_i)$ .

…

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CBSE 2018Set ANNUAL2 marksMCQ
$P(x) = \dfrac{3-x}{10}$
(a) 1
(b) 2
(c) 0
(d) -1
›Reveal solutionSolution

Compute each probability from the p.m.f., then $E(X)=\sum x\,P(x)$ .

$P(-1)=\frac{3-(-1)}{10}=\frac{4}{10}=0.4,\quad P(0)=\frac{3}{10}=0.3,\quad P(1)=\frac{2}{10}=0.2,\quad P(2)=\frac{1}{10}=0.1$

(Check: $0.4+0.3+0.2+0.1=1$ ✓, a valid p.m.f.)

…

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CBSE 2017Set ANNUAL2 marksMCQ
$Q. The expected value of the number of heads obtained when three fair coins are tossed simultaneously is$
(a) $1$
(b) $1.5$
(c) $0$
(d) $-1$
›Reveal solutionSolution

$X\sim B(3,\tfrac12)$ ; expected value $E(X)=np$ .

…

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