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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 μ.

μ = ∑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) = μ = ∑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


μ = ∑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 (μ) = 1.5

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