Question

Let X be a discrete random variable with the following p.m.f
`"P"(x) = {{:(0.3,  "for"  x = 3),(0.2,  "for"  x = 5),(0.3,  "for"  x = 8),(0.2,  "for"  x = 10),(0,  "otherwise"):}`
Find and plot the c.d.f. of X.

Answer 1

F(3) = P(x ≤ 3)

= P(3)

= 0.3

F(5) = P(x ≤ 5)

= P(x = 3) + (x = 5)

= 0.3 + 0.2

= 0.5

F(8) = P(x ≤ 8)

= P(3) + P(5) + P(8)

= 0.3 + 0.2 + 0.3

= 0.8

F(10) = P(x ≤ 10)

= P(3) + P(5) + P(8) + P(10)

= 0.3 + 0.2 + 0.3 + 0.2

= 1

`"F"_x(x) = {{:(0,  "for"  x < 3),("P"_x(3) = 0.3,  "for"  3 ≤ x < 5),("P"_x(3) + "P"_x(5) = 0.5,  "for"  5 ≤ x < 8),("P"_x(3) + "P"_x(5) + "P"_x(8) = 0.8,  "for"  8 ≤ x < 10),(1,  "for"  x ≥ 10):}`