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.

Answer 1

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`.