Sum

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)

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#### Solution

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

Comparing with p(x) = `("n"/"x")("p")^"x"("q")^("n"-"x")`

`therefore "n" = 4 , "p" = 5/9 , "q"=4/9`

E(x) = np = `4xx5/9 = 20/9`

V(x) = npq = `4xx5/9xx4/9 = 80/81`

Concept: Probability Distribution - Probability Mass Function (P.M.F.)

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