Business Analytics > Probability, Risk & Sampling > Variance of a Discrete Random Variable

Variance of a Discrete Random Variable

Variance of a discrete random variable X as a weighted average of the squared deviations from the expected value:

Variance measures the uncertainty of the random variable. The higher the variance, the higher the uncertainty of the outcome. We usually measure the variability of a random variable by its standard deviation, which is simply the square root of the variance.

Example: The previous statistics says that Bangladesh cricket team got wickets in the world cup semi-final zero, one, two, three, four, five, six, seven .. ten wickets with the following probabilities.

Number of wickets (x)	Probabilities p(x)	x. p(x)
0	0.01	0	0
1	0.05	0.05	0.828245
2	0.09	0.18	1.696482
3	0.12	0.36	1.542564
4	0.17	0.68	0.778532
5	0.16	0.8	0.00392
6	0.14	0.84	0.726516
8	0.11	0.88	7.554712
8	0.09	0.72	6.181128
9	0.04	0.36	5.560164
10	0.02	0.2	4.86098
	Total () =	5.07	29.733243

So variance= 29.73 and Standard Deviation = 5.45281973

Rule of thumb is: Variance is considered less i.e. dispersion is less if standard deviation is less than the half of the mean otherwise dispersion is high. Here dispersion is high i.e. performance is unpredictable or uncertain.

 

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