Sum

A random variable X has the following probability distribution :

X |
0 | 1 | 2 | 3 | 4 | 5 | 6 |

P(X) |
C | 2C | 2C | 3C | C^{2} |
2C^{2} |
7C^{2}+C |

Find the value of C and also calculate the mean of this distribution.

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#### 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`.

Concept: Random Variables and Its Probability Distributions

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