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

${\displaystyle P(x\ge 2)=0.3+0.4+0.2=0.9}$
${\displaystyle f\left(x_i\right)=P_1+P_2+P_3+\dots \dots .+P_i}$ where, i = 1, …, x

Thus ${\displaystyle f\left(x_1\right)=P_1=0.1}$

${\displaystyle f\left(x_2\right)=P_1=0.1}$

${\displaystyle f\left(x_2\right)=P_1+P_2=0.1+0.3=0.4}$

${\displaystyle f\left(x_3\right)=P_1+P_2+P_3=0.1+0.3+0.4=0.8}$

${\displaystyle f\left(x_4\right)=P_1+P_2+P_3+P_4=0.1+0.3+0.4+0.2=1}$

${\displaystyle \therefore f\left(x_4\right)=\sum _{i=1}^4{P}_i=1}$

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