Pdf of rv X is given by fx find the value of constant c expe

P.d.f of r.v X is given by f(x)= find the value of constant c; expected value of X; c.d.f ofX.

Solution

a)

Normalizing,

c(1) + c(2) + c(3) = 1

6c = 1

c = 1/6 [ANSWER]

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b)

E(X) = Sum (x f(x)) = 1(1/6) + 2(2/6) + 3(3/6) = 7/3 or 2.3333333 [ANSWER]

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c)

Adding up probabilities to get the cdf,

F(x) = 0, x < 1
1/6, x = 1
1/2, x = 2
1, x >= 3 [ANSWER]