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प्रश्न
The cumulative distribution function of a discrete random variable is given by
F(x) = `{{:(0, "for" - oo < x < 0),(1/2, "for" 0 ≤ x < 1),(3/5, "for" 1 ≤ x < 2),(4/5, "for" 2 ≤ x < 4),(9/5, "for" 3 ≤ x < 4),(1, "for" ≤ x < oo):}`
Find the probability mass function
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उत्तर
F(1) = P(X = 0)
= F(0) – F(0)
= `1/2 - 0`
F(1) = P(X = 1)
= F(1) – F(0)
= `3/5 - 1/2 = 1/10`
F(2) = P(X = 2)
= F(2) – F(1)
= `4/5 - 3/5`
= `1/5`
F(3) = P(X = 3)
= F(3) – F(2)
= `9/10 - 4/5`
= `1/10`
F(4) = P(X = 4)
= F(4) – F(3)
= `1 - 9/10`
= `1/10`
Probability mass function
| x | 0 | 1 | 2 | 3 | 4 |
| F(x) | `1/2` | `1/10` | `1/5` | `1/10` | `1/10` |
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