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Question
The probability function of a random variable X is given by
p(x) = `{{:(1/4",", "for" x = - 2),(1/4",", "for" x = 0),(1/2",", "for" x = 10),(0",", "elsewhere"):}`
Evaluate the following probabilities
P(|X| ≤ 2)
Solution
| X | – 2 | 0 | 10 |
| P(X = x) | `1/4` | `1/4` | `1/2` |
P(|x| ≤ 2) = P(– 2 ≤ X ≤ 2)
= P(X = – 2) + P(X = 0)
= `1/4 + 1/4`
= `2/4`
= `1/2`
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