Question

ASAP

Consider the discrete random variable XX given in the table below. Calculate the mean, variance, and standard deviation of XX.

XX	1	10	12	14	15	17	18
P(XX)	0.12	0.14	0.27	0.13	0.1	0.14	0.1

μμ = Incorrect
σ2σ2 = Incorrect
σσ = Incorrect


What is the expected value of X?

Answer 1

Solution :

x	P(x)	x * P(x)	x2 * P(x)
1	0.12	0.12	0.12
10	0.14	1.4	14
12	0.27	3.24	38.88
14	0.13	1.82	25.48
15	0.1	1.5	22.5
17	0.14	2.38	40.46
18	0.1	1.8	32.4
Sum	1	12.26	173.84

Mean = = X * P(X) = 12.26

The expected value of X = 12.26

Variance = = X ² * P(X) - ²  = 173.84 - 12.26² = 23.5324

Standard deviation =

=X ² * P(X) - ²

=  23.5324

= ​​​​​​​4.851