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Question
A random variable X has the following probability distribution :
| X | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| P(X) | C | 2C | 2C | 3C | C2 | 2C2 | 7C2+C |
Find the value of C and also calculate the mean of this distribution.
Solution
As `sum "P"("X") = 1`
∴ `"C" + 2"C" + 2"C" + 3"C" + "C"^2 + 2"C"^2 + 7"C"^2 + "C" = 1`
⇒ `10"C"^2 + 9"C" -1 = 0`
⇒ `(10"C" -1)("C" + 1)= 0`
∵ `"C" != -1`
so, `"C" = (1)/(10)`.
Also mean = `sum "X""P"("X") = 0 xx "C" + 1 xx 2"C" + 2 xx 2"C" + 3 xx 3"C" + 4 xx "C"^2 + 5 xx 2"C"^2 + 6 xx (7"C"^2 + "C")`
⇒ = `21"C" + 56"C"^2 = 56 xx (1)/(100) + 21 xx (1)/(10) = (266)/(100) or 2.66`.
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