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# Mean of a Random Variable

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#### Mean of a Random Variable - Lesson Summary

Mean is the middle or average value of a random variable.

The mean of a random variable is denote by Î¼.

Î¼ = âˆ‘i=1n xipi

X or Xi

x1

x2

x3

...

xn

P(X) or pi

p1

p2

p3

...

pn

The mean of random variable X is also called the expectation of X, and is denoted by E(X).

E(X) = Î¼ = âˆ‘i=1n xipi = x1p1 + x2p2 + x3p3 + .... + xnpn

Ex:

Consider an experiment of tossing three coins simultaneously.

S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

X denotes the number of heads in each outcome.

The possible values of X are 0, 1, 2 and 3.

Probability distribution of X:

X or xi

0

1

2

3

P(X) or pi

1/8

3/8

3/8

1/8

Î¼ = âˆ‘i=14 xipi = x1p1 + x2p2 + x3p3 + x4p4

= (0 x 1/8) + (1 x 3/8) + (2 x 3/8) + (3 x 1/8)

= 0 + 3/8+ 6/8+ 3/8

= 12/8 = 1.5

Hence, mean of random variable X (Î¼) = 1.5