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Question: Random variable X has its range = {0, 1, 2} and their probabilities are given by P(x=0) = 3k<sup>3</...

Random variable X has its range = {0, 1, 2} and their probabilities are given by P(x=0) = 3k3, P(x=1) = 4k – 10k2. P(x=2) = 5k-1 Then SD is.

A

38/81

B

14\sqrt { 14 }/3

C

14/9

D

38\sqrt { 38 }/9

Answer

38\sqrt { 38 }/9

Explanation

Solution

μ = 29+129=149\frac { 2 } { 9 } + \frac { 12 } { 9 } = \frac { 14 } { 9 }

σ2 = (−149)2×19+(59)2×29+(49)223×33\left( \frac { - 14 } { 9 } \right) ^ { 2 } \times \frac { 1 } { 9 } + \left( \frac { 5 } { 9 } \right) ^ { 2 } \times \frac { 2 } { 9 } + \left( \frac { 4 } { 9 } \right) ^ { 2 } \frac { 2 } { 3 } \times \frac { 3 } { 3 }

= 196+50+96729=342729=3881\frac { 196 + 50 + 96 } { 729 } = \frac { 342 } { 729 } = \frac { 38 } { 81 }

σ = 389\frac { \sqrt { 38 } } { 9 }