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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 the value of k
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Solution
Given f is a probability mass function
`sum_x "f"(x)` = 1
Probability mass function is
| x | 0 | 1 | 2 |
| F(x) | `1/k` | `2/k` | `5/k` |
`1/k + 2/k + 5/k` = 1
`8/k` = 1
k = 8
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