Question

Let x be a discrete random variable with the following probability distribution

x: -1 , 0 , 1, 2

P(x) 0.3 , 0.2 , 0.15 , 0.35

Find the mean and the standard deviation of x

Answer 1

Solution:

Let mean is given by Mean = x * P(x) = [ (-1 * 0.3) + (0 * 0.2) + (1 * 0.15) + (2*0.35)],

calculations are shown in below table;

xi	pi	xi * pi	xi^2 * pi
-1	0.3	-0.3	0.3
0	0.2	0	0
1	0.15	0.15	0.15
2	0.35	0.7	1.4
	Totals	0.55	1.85

Hence mean = 0.55

Now Standard Deviation = sqrt(variance)

where variance = xi ^2 * pi - (mean)^2 = 1.85 - 0.55² = 1.5475

Hence standard deviation = sqrt ( 1.5475) = 1.2440

Thanks ! Best Luck !