HSC Science (Electronics) 12th Board ExamMaharashtra State Board
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# Solution - 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 (Electronics) 12th Board Exam - Mathematics and Statistics

#### 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

Is there an error in this question or solution?

#### 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: null - Probability Mass Function (P.M.F.). For the courses HSC Science (Electronics), HSC Science (Computer Science), HSC Arts, HSC Science (General)
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