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Question
The cumulative distribution function of a discrete random variable is given by
F(x) = `{{:(0, - oo < x < - 1),(0.15, - 1 ≤ x < 0),(0.35, 0 ≤ x < 1),(0.60, 1 ≤ x < 2),(0.85, 2 ≤ x < 3),(1, 3 ≤ x < oo):}`
Find the probability mass function
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Solution
Given F(x) = `{{:(0, - oo < x < - 1),(0.15, - 1 ≤ x < 0),(0.35, 0 ≤ x < 1),(0.60, 1 ≤ x < 2),(0.85, 2 ≤ x < 3),(1, 3 ≤ x < oo):}`
The value of 'x' are –1, 0, 1, 2, 3
F(–1) = P(X = –1)
= F(–1) – F(–1)
= 0.15 – 0
= 0.15
F(0) = P(X = 0)
= F(0) – F(–1)
= 0.35 – 0.15
= 0.20
F(1) = P(X = 1)
= F(1) – F(0)
= 0.60 – 0.35 =
0.25
F(2) = P(X = 2)
= F(2) – F(1)
= 0.85 – 0.60
= 0.25
F(3) = P(X = 3)
= F(3) – F(2)
= 1 – 0.85
= 0.15
Probability mass function table
| x | –1 | 0 | 1 | 2 | 3 |
| F(x) | 0.15 | 0.20 | 0.25 | 0.25 | 0.15 |
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