# Find k, such that the function  P(x)=k(4/x) ;x=0,1,2,3,4 k>0 - Mathematics and Statistics

Find k, such that the function  P(x)=k(4/x) ;x=0,1,2,3,4 k>0

=0 ,otherwise

#### Solution

P(x)=k(4/x) ;x=0,1,2,3,4 k>0

=0 ,otherwise

P(X = 0) = k^4C_0 = k(1) = k

P(X = 1) = k^4C_1 = k(4) = 4k

P(X = 2) = k^4C_2 = k(6) = 6k

P(X = 3) = k^4C_3 = k(4) = 4k

P(X = 4) = k^4C_4 = k(1) = k

 X 0 1 2 3 4 P(X = x): k 4k 6k 4k k

Since, the function represents a p.m.f.

sum_(x=0)^4P(X=x)=1

k + 4k + 6k + 4k + k = 1
16k = 1

k = 1/16

Concept: Standard Deviation of Binomial Distribution (P.M.F.)
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