Mean (Expectation), Variance from a Probability Distribution of a Discrete Random Variable

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If x is a random variable, show that
(i) E(1) = 1; (ii) E(3x) = 3E(x) and (iii) E(2 + 3x) = 2 + 3E(x)

Net Answers :

Solution

We know, E (x) = Σ px
Therefore,

(i)

E (1) = Σ p × 1

= Σ p

= 1

(ii)

E (3x) = Σ p × 3x

= 3 Σ px

= 3 E(x)

(iii)

E (2 + 3x) = Σ p (2 + 3x)

= Σ (2p + 3px)

= Σ 2p + Σ 3px

= 2 × Σ p + 3 × Σ px

= 2 × 1 + 3 × E (x)

= 2 + 3 E (x)

Credit : Vijayalakshmi Desu

Probability Distribution Mean (Expectation), Variance :: Problems