Question

Given the following discrete probability distribution, calculate the variance of the random variable X. Round your answer to 2 significant places after the decimal.

x P(x)

-2 0.15

3 0.43

5 0.16

6 0.26

Answer 1

Solution:

For variance we need to calculate mean for this discrete distribution

X	P(X)	Xi*P(Xi)
-2	0.15	-0.3
3	0.43	1.29
5	0.16	0.8
6	0.26	1.56

Expected mean = summation(Xi*P(Xi)) = -0.3+1.29+0.8+1.56 = 3.35

Variance can be calculated as = summation(Xi-mean)^2*P(Xi)

X	P(X)	Xi*P(Xi)	Xi-mean	(Xi-mean)^2	(Xi-mean)^2 *P(Xi)
-2	0.15	-0.3	-5.35	28.6225	4.293375
3	0.43	1.29	-0.35	0.1225	0.052675
5	0.16	0.8	1.65	2.7225	0.4356
6	0.26	1.56	2.65	7.0225	1.82585

Variance = (4.293375+0.052675+0.4356+1.82585) = 6.61