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Question
Suppose a discrete random variable can only take the values 0, 1, and 2. The probability mass function is defined by
`f(x) = {{:((x^2 + 1)/k"," "for" x = 0"," 1"," 2),(0"," "otherwise"):}`
Find cumulative distribution function
Solution
F(0) = P(x ≤ 0)
= P(x = 0)
= `1/8`
F(1) = P(x ≤ 1)
= P(x = 0) + P(x = 1)
= `1/8 + 2/8`
= `3/8`
F(2) = P(x ≤ 2)
= P(x = 0) + P(x = 1) + P(x = 2)
= `1/8 + 2/8 + 5/8`
= 1
| x | 0 | 1 | 2 |
| F(x) | `1/8` | `3/8` | 1 |
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