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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

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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`
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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
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