Question

Evaluate the cumulative distribution function of a binomial random variable with n equals 3 and p equals 1/3 at specified points. Give exact answers in form of fraction. Upper F(0 ) equals Upper F(1) equals Upper F (2) equals Upper F(3)

Answer 1

Answer:

Given That,

n=3,p=1/3

Then,

q=1-p

=1-(1/3)

=2/3

It follows binomial distribution

Now, we have to find,

(1). F(0):

F(0)=P(X0)

=8/27

(2).F(1):

F(1)=P(X1)

=P(X=0)+P(X=1)

=20/27

(3).F(2):

F(2)=P(X2)

=P(X=0)+P(X=1)+P(X=2)

=26/27

(4).F(3):

F(3)=P(X3)

=P(X=0)+P(X=1)+P(X=2)+P(X=3)

=27/27

=1