Discrete random variables- Cumulative Distribution Function

Question

QUESTION 1:
The discrete random variable X has the following probability distribution function.
f(x)={■(1/6&x=0,2@1/3&x=1,3@0&otherwise)}
(a) Find the cumulative distribution function F(x)
(b) P(X≤2)
(c) P(X<1)
(d) P(0<X≤3)
(e) P(X>2)
(f) P(X<-1)

QUESTION 2:
The discrete random variable X has the following probability distribution function.
f(x)={■(1/8&x=0,3@3/8&x=1,2@0&otherwise)}
(a) Find the cumulative distribution function F(x)
(b) P(X≤-0.5)
(c) P(X≤2.5)
(d) P(X≤4)

QUESTION 3
The cumulative distribution function F(x) of a discrete random variable X is given by:
F(x)=kx,x=1.2,3,4
Find
(a) the value of the constant k
(b) the probability distribution of X

Answer 1

ANSWER 1:
(a) F(x) = {■(0&x<0@1/6&x=0@2/3&x=1@1&x=2@1&x>2)}
(b) P(X≤2) = 1
(c) P(X<1) = 2/3
(d) P(0<X≤3) = 1
(e) P(X>2) = 0
(f) P(X<-1) = 0

ANSWER 2:
(a) F(x) = {■(0&x<0@1/8&x=0@4/8&x=1@7/8&x=2@1&x>2)}
(b) P(X≤-0.5) = 0
(c) P(X≤2.5) = 1
(d) P(X≤4) = 1

ANSWER 3:
(a) The value of the constant k = 1/4
(b) The probability distribution of X = {■(1/4&x=1@1/2&x=2@3/4&x=3@1&x=4)}