Question

A random variable X has the following probability distribution :

X=x	0	1	2	3	4	5	6
P[X=x]	k	3k	5k	7k	9k	11k	13k

(a) Find k
(b) find P(O <X< 4)
(c) Obtain cumulative distribution function (c. d. f.) of X.

Answer 1

sum P(x)=1

P(0)+P(1)+P(2)+P(3)+P(4)+P(5)+P(6)=1

K+3x +5k +7k +9k +11k +13k=1

49k=1

k=1/49

P(0<x<4)=P(1)+P(2)+p(3)

=3k+5k+7k

=15k

=15/49

`F(0)=P(0)=1/49`

`F(1)=P(0)+P(1)=1/49+3/49=4/49`

`F(2)=P(0)+P(1)+P(2)=1/49+3/49+5/49=9/49`

`F(3)=P(0)+P(1)+P(2)+P(3)=1/49+3/49+5/49+7/49=16/49`

`F(4)=P(0)+P(1)+P(2)+P(3)+P(4)=1/49+3/49+5/49+7/49+9/49=25/49`

`F(5)=P(0)+P(1)+P(2)+P(3)+P(4)+P(5)=1/49+3/49+5/49+7/49+9/49+11/49=36/49`

`F(6)=P(0)+P(1)+P(2)+P(3)+P(4)+P(5)+P(6)=1/49+3/49+5/49+7/49+9/49+11/49+13/49=49/49`

 Cummulative districbution function (c.d.f.) of x

X	0	1	2	3	4	5	6
F(x)	1/49	4/49	9/49	16/46	25/49	36/49	1