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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.
Solution
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):}`
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