The discrete random variable X has the probability fuction f

The discrete random variable X has the probability fuction

for all other x.

(a) Find c

(b) Find Cumulative distribution fuction

Solution

a)

Normalizing,

f(1) + f(2) + f(3) + f(4) = 1

1/c + 2/c + 3/c + 4/c = 1

10/c = 1

c = 10 [ANSWER]

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b)

Thus,

F(x) = 0, x<1
1/10, x = 1
3/10, x = 2
3/5, x = 3
1, x >= 4 [ANSWER]