Question

Probability distribution of X is given by

X = x	1	2	3	4
P(X = x)	0.1	0.3	0.4	0.2

Find P(X ≥ 2) and obtain cumulative distribution function of X

Answer 1

By definition cummulative distribution function at x is

`P(x ≥ 2) = 0.3 + 0.4 + 0.2 = 0.9`
`f (x_i) = P_1 + P_2 + P_3 + ……. + P_i` where, i = 1, …, x

Thus `f(x_1)=P_1=0.1`

`f(x_2)=P_1=0.1`

`f(x_2)=P_1+P_2=0.1+0.3=0.4`

`f(x_3)=P_1+P_2+P_3=0.1+0.3+0.4=0.8`

`f(x_4)=P_1+P_2+P_3+P_4=0.1+0.3+0.4+0.2=1`

`therefore f(x_4)=sum_(i=1)^4P_i=1`

X = x	1	2	3	4
P(X = x)	0.1	0.4	0.8	1