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Question
The probability distribution of X is as follows:
| X | 0 | 1 | 2 | 3 | 4 |
| P(X = x) | 0.1 | k | 2k | 2k | k |
Find k and P[X < 2]
Solution
As probability distribution of r. v. X is given, `sum"P"("X" = x)` = 1
i.e., P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 1
∴ 0.1 + k + 2k + 2k + k = 1
∴ 6k = 0.9
∴ k = 0.15 .....(i)
∴ P[X < 2] = P(X = 0 or 1)
= P(X = 0) + P(X = 1)
= 0.1 + k
= 0.1 + 0.15 ......[From (i)]
= 0.25
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The probability distribution of X is as follows:
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