The cumculative distribution function of a discrete random variable is given by
`F(x)={{:(0, -infty lt x lt -1), (0.15, -1 le x lt 0), (0.35, 0 le x lt 1), (0.60, 1 le x lt 2), (0.85, 2 le x lt 3), (1, 3 le x lt infty):}`
Find (i) the probability mass function (ii) `P(X lt 1)` and (iii) `P(X ge 2)`.

The cumculative distribution function of a discrete random variable is given by F(x)={{:(0, "for "-infty lt x lt 0), ( 1/2, "for " 0 le x lt 1), (3/5, "for " 1 le x lt 2), (4/5, "for " 2 le x lt 3), (9/10, "for " 3 le x lt 4), (1, "for " 4 le x lt infty):} Find (i) the probability mass function (ii) P(X lt 3) and (iii) P(X ge 2) .

Find the rpobability mass function f(x) of the discrete random variable X whose cumulative distribution function f(x) is given by {{:(0,-inftylt x lt -2),(0.3,-2lexlt-1),(0.45,-1lexlt0),(0.7,0lexlt1),(1,1lexltinfty):} Also find P(x lt 0)

If X is the random varibale with distribution function F(x) given by F(x)={{:(0,-inftyltxlt0),(3/2(x-(x^(3))/(3)),0lexlt1),(1,3lexltinfty):} Find P(0.3 lt x lt 0.5)

Discuss the continuity of the function f, where f is defined by f(x)={{:(3," if "0 le xle 1),(4," if "1 lt x lt 3),(5," if "3 le x le 10):} .

A random varibale x has the following probability mass function P(2 le X lt5)

The probability density function of X is f(x)={{:(x, 0 lt x lt 1), (2-x, 1 le x lt 2), (0, "otherwise"):} Find P(0.5 le X lt 1.5)

The probability density function of X is f(x)={{:(x, 0 lt x lt 1), (2-x, 1 le x lt 2), (0, "otherwise"):} Find P(0.2 le X lt 0.6)

The probability density function of X is f(x)={{:(x, 0 lt x lt 1), (2-x, 1 le x lt 2), (0, "otherwise"):} Find P(1.2 le X lt 1.8)

Discuss the continuity of the function f, where f is defined by f(x)={{:(-2," if "x le -1),(2x," if "-1 lt x le 1),(2," if "x gt 1):} .