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Tamil Nadu Board of Secondary EducationHSC Science Class 12

For the random variable X with the given probability mass function as below, find the mean and variance. ,,otherwisef(x)={4-x6 x=1, 2, 30 otherwise

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Question

For the random variable X with the given probability mass function as below, find the mean and variance.

`f(x) = {{:((4 - x)/6,  x = 1","  2","  3),(0,  "otherwise"):}`

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Solution

Probability mass function

x 1 2 3
F(x) `1/2` `1/3` `1/6`

Mean: `mu = "E"("X")`

= `sum x f(x)`

= `1 xx 1/2 + 2 xx 1/3 + 3 xx 1/6`

= `1/2 + 2/3 + 3/6`

= `10/6`

= 1.67

Variance: `"E"("X"^2)`

= `1^2 xx 1/2 + 2^2 xx 1/3 + 3^2 xx 1/6`

= `1/2 + 4/3 + 9/6`

= `20/6`

= 3.33

Var (X) = E(X2) – [E(X)]2

= 3.33 – (1.67)2

= 3.33 – 2.79

= 0.54

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Mathematical Expectation
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Chapter 11: Probability Distributions - Exercise 11.4 [Page 210]

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Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 12 TN Board
Chapter 11 Probability Distributions
Exercise 11.4 | Q 1. (ii) | Page 210

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