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Question
Probability distribution of X is given by
| X = x | 1 | 2 | 3 | 4 |
| P(X = x) | 0.1 | 0.3 | 0.4 | 0.2 |
Find P(X ≥ 2) and obtain cumulative distribution function of X
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Solution
By definition cummulative distribution function at x is
`P(x ≥ 2) = 0.3 + 0.4 + 0.2 = 0.9`
`f (x_i) = P_1 + P_2 + P_3 + ……. + P_i` where, i = 1, …, x
Thus `f(x_1)=P_1=0.1`
`f(x_2)=P_1=0.1`
`f(x_2)=P_1+P_2=0.1+0.3=0.4`
`f(x_3)=P_1+P_2+P_3=0.1+0.3+0.4=0.8`
`f(x_4)=P_1+P_2+P_3+P_4=0.1+0.3+0.4+0.2=1`
`therefore f(x_4)=sum_(i=1)^4P_i=1`
| X = x | 1 | 2 | 3 | 4 |
| P(X = x) | 0.1 | 0.4 | 0.8 | 1 |
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