HSC Science (Computer Science) 12th Board ExamMaharashtra State Board
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Solution for Let the p. m. f. (probability mass function) of random variable x be p(x)=(4/x)(5/9)^x(4/9)^(4-x), x=0, 1, 2, 3, 4 =0 otherwise find E(x) and var (x) - HSC Science (Computer Science) 12th Board Exam - Mathematics and Statistics

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Question

Let the p. m. f. (probability mass function) of random variable x be

`p(x)=(4/x)(5/9)^x(4/9)^(4-x), x=0, 1, 2, 3, 4`

         =0 otherwise

find E(x) and var (x)

Solution

`p(x)=(4/x)(5/9)^x(4/9)^(4-x)`

The probability distribution table of the function is

 

Xi 0 1 2 3 4
P(Xi)

`oo`

`1280/6561`

`1600/(6561xx2)`

`2000/(6561xx3)`

`625/6561`

`P(x_i)X_i^2`

0

`1280/6561`

`3200/6561`

`6000/6561`

`10000/6561`

`E(X)=x_1xxP(x_1)+x_2xxP(x_2)+x_3xxP(x_3)+x_4xxP(x_4)+x_5xxP(x_5))`

`=0xxoo+1xx4/1xx5/9xx(4/9)^3+2xx4/2xx(5/9)^2xx(4/9)^2+3xx4/3xx(5/9)^3xx(4/9)^1+4xx4/4xx(5/9)^4xx(4/9)^0`

`=0+1280/6561+1600/6561+2000/6561+2500/6561`

`=7380/6561=1.12`

`Var(x)=sumP(X_i)X_i^2-[E(X)]^2`

`=1280/6561+3200/6561+6000/6561+10000/6561-1.12`

`=20480/6561-1.12`

`=3.12-1.12`

=2

 

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APPEARS IN

 2014-2015 (March) (with solutions)
Question 6.1.3 | 3 marks

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Solution for question: Let the p. m. f. (probability mass function) of random variable x be p(x)=(4/x)(5/9)^x(4/9)^(4-x), x=0, 1, 2, 3, 4 =0 otherwise find E(x) and var (x) concept: Probability Distribution - Probability Mass Function (P.M.F.). For the courses HSC Science (Computer Science), HSC Science (General) , HSC Arts, HSC Science (Electronics)
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