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Question: If the difference between Mean and variance of 5 traits is 5/9, find P (X=2) =...

If the difference between Mean and variance of 5 traits is 5/9, find P (X=2) =

A

100/243

B

80/243

C

163/243

D

143/243

Answer

80/243

Explanation

Solution

n = 5

np = npq = 5/9

p(1-q) = 19\frac { 1 } { 9 } . P2 = 19,P=13,q=23\frac { 1 } { 9 } , \mathrm { P } = \frac { 1 } { 3 } , \mathrm { q } = \frac { 2 } { 3 }

P(X=2) = 5C2(13)2⋅(23)3=10×835=80243{ } ^ { 5 } \mathrm { C } _ { 2 } \left( \frac { 1 } { 3 } \right) ^ { 2 } \cdot \left( \frac { 2 } { 3 } \right) ^ { 3 } = \frac { 10 \times 8 } { 3 ^ { 5 } } = \frac { 80 } { 243 }