comulative distribution

Definition:-
The cumulative dis, function (CDF) F(x) for a random variable X is defined as
F(x)= p(X?x), if X is discrete F(x)=?_(y?x)??p(y)? , where p(x) is the probability mass function .
Example: - Find CDF of the random variable from above example using F(x), verify that p(X=1=15/28).
SOL:-
The CDF of the random variable X is:
X 0 1 2
P(X) 10/28 15/28 3/28

F(0)=P(0)=10/28
F(1)=P(0)+P(1)=25/28
F(2)=P(0)+P(1)+P(2)=28/28=1

F(x)={?(0 for x<0@10/28 for 0?x<1@25/28 for 1?x<2@1 for x?2)?
Now, p(X=1)=p(1)=F(1)-F(0)=25/28-10/28=15/28
Graphically , p(x) can be represented as a probability histogram where the heights of the bar are equal to p(x)Definition:-
The cumulative dis, function (CDF) F(x) for a random variable X is defined as
F(x)= p(X?x), if X is discrete F(x)=?_(y?x)??p(y)? , where p(x) is the probability mass function .
Example: - Find CDF of the random variable from above example using F(x), verify that p(X=1=15/28).
SOL:-
The CDF of the random variable X is:
X 0 1 2
P(X) 10/28 15/28 3/28

F(0)=P(0)=10/28
F(1)=P(0)+P(1)=25/28
F(2)=P(0)+P(1)+P(2)=28/28=1

F(x)={?(0 for x<0@10/28 for 0?x<1@25/28 for 1?x<2@1 for x?2)?
Now, p(X=1)=p(1)=F(1)-F(0)=25/28-10/28=15/28
Graphically , p(x) can be represented as a probability histogram where the heights of the bar are equal to p(x)