# Find the expected value, variance and standard deviation of the random variable whose p.m.f.’s are given below : x = x -1 0 3 P (X = x) 15 25 25 - Mathematics and Statistics

Sum

Find the expected value, variance and standard deviation of the random variable whose p.m.f.’s are given below :

 x = x -1 0 3 P (X = x) 1/5 2/5 2/5

#### Solution

We construct the following table to find the expected value, variance and standard deviation:

 xi P (xi) xi·P (xi) xi 2·P (xi) = xi × xi·P (xi) -1 1/5 -1/5 1/5 0 2/5 0 0 1 2/5 2/5 2/5 Total 1 1/5 3/5

From the table,

∑xi·P (xi) = 1/5,

∑ xi 2·P (xi) = 3/5

Expected value = E (X) = ∑xi·P (xi) = 1/5 = 0.2

Variance = V (x) = ∑ xi 2·P (xi)  - [ ∑xi·P (xi) ]2

= 3/5 - (1/5)^2

= 3/5 - 1/25

= 15/25 - 1/25

= 14/25

= 0.56

Standard deviation = sqrt(V(X)

= sqrt(0.56)

= 0.7483

Concept: Variance of a Random Variable
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 7 Probability Distributions
Miscellaneous Exercise 2 | Q 10.2 | Page 244