Question

Find the mean and standard deviation of each of the following probability distributions:

Xi:	-3	-1	0	1	3
Pi:	0.05	0.45	0.20	0.25	0.05

Answer 1

Mean of any probability distribution is given by Mean = ∑x_ip_i

Standard Deviation is given by SD = √ Variance where variance is given by:

Variance = ∑x_i²p_i – (∑x_ip_i)²

∴ first we need to find the products i.e. p_ix_i and p_ix_i² and add them to get mean and apply the above formula to get the variance.

Following table gives the required products :

∴ mean = -0.15 - 0.45 + 0 + 0.25 + 0.15 = -0.2

And variance = 0 + 0.45 + 0.25 + 0.45 + 0.45 – (-0.2)² = 1.56

∴ Standard deviation = √1.56 = 1.248