Question

Probability distribution of X is given by

Find `P(X le 2)` and obtain cumulative distribution function of X.

Answer 1

By definition , cumulative function at `x_(i)` is
`f(x_(i)) = p_(1)+p_(2) + .........p_(i) , i = 1,2 .........n`
Thus`, f(x_(1)) = 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_($) = 0.1 + 0.3 + 0.4 + 0.2 = 1.0`

`P(X ge 2) = 1 - P(X lt 2)`
` = 1- P(X = 1)`
` =1- 0.1 = 0.9`