# 70% of the members favour and 30% oppose a proposal in a meeting. The random variable X takes the value 0 if a member opposes the proposal and the value 1 if a member is in favour. Find E(X) - Mathematics and Statistics

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70% of the members favour and 30% oppose a proposal in a meeting. The random variable X takes the value 0 if a member opposes the proposal and the value 1 if a member is in favour. Find E(X) and Var(X).

#### Solution

According to the given conditions,

P(X = 0) = (30)/(100) = (3)/(10)  "and"  "P"("X" = 1) = (70)/(100) = (7)/(10)

∴ E(X) = $\sum\limits_{i=1}^{2} x_i\text{P}(x_i)$ = 0 xx (3)/(10) + 1 xx (7)/(10) = (7)/(10) = 0.7

∴ E(X2) = $\sum\limits_{i=1}^{2} x_i^2\text{P}(x_i)$ = 0^2 xx (3)/(10) + 1^2 xx (7)/(10) = (7)/(10) = 0.7

∴ Var(X) = E(X2) – [E(X)]2 = (7)/(10) - (7/10)^2

= (70 - 49)/(100)

= (21)/(100)
= 0.21

Concept: Probability Distribution of Discrete Random Variables
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Probability Distributions
Exercise 8.1 | Q 1.16 | Page 141