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) - Mathematics and Statistics

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)

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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