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For the following probability distribution determine

Question:

For the following probability distribution determine standard deviation of the random variable X.

Solution:

We know that: Standard deviation (S.D.) = √Variance

So, Var(X) = E(X2) – [E(X)]2

E(X) = 2 x 0.2 + 3 x 0.5 + 4 x 0.3 = 0.4 + 1.5 + 1.2 = 3.1

E(X2) = 4 x 0.2 + 9 x 0.5 + 16 x 0.3 = 0.8 + 4.5 + 4.8 = 10.1

⇒ V(X) = 10.1 – (3.1)2 = 10.1 – 9.61 = 0.49

Therefore, S.D. = √0.49 = 0.7

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