Q. 495.0( 1 Vote )

# Let X be a discre

Answer :

Given: Thus, we have the probability distribution of X is (i) the value of k

We know that,

Sum of the probabilities = 1 2k + 3k + 4k + 5k + 10k + 12k + 14k = 1

50k = 1 k = 0.02

(ii) To find: E(X)

The probability distribution of X is: Therefore,

μ = E(X) E(X) = 2k + 6k + 12k + 20k + 50k + 72k + 98k + 0

= 260k  = 5.2 …(i)

(iii) To find: Standard deviation of X We know that,

Var(X) = E(X2) – [E(X)]2

= ΣX2P(X) – [Σ{XP(X)}]2

= [2k + 12k + 36k + 80k + 250k + 432k + 686k +0] – [5.2]2 = 1498k – 27.04 = 29.96 – 27.04

= 2.92

We know that,

standard deviation of X = √Var(X) = √2.92 = 1.7088

1.7

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