The expectation of a random variable X w

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Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Probability Distributions

Question:

The expectation of a random variable X with following distribution :

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

is :

Options:

0.5

1.5

2.5

3.5

Correct Answer:

1.5

Explanation:

The correct answer is Option (2) → 1.5

The expectation (Mean) of a discrete random variable,

$E(X)=∑X.P(X)$

$=\left(0×\frac{1}{6}\right)+\left(1×\frac{2}{6}\right)+\left(2×\frac{2}{6}\right)+\left(3×\frac{1}{6}\right)$

$=\frac{2+4+3}{6}=\frac{9}{6}=1.5$