Question

A discrete random variable X has the following probability distribution:

X	1	2	3	4	5	6	7
P(X)	C	2C	2C	3C	C2	2C2	7C2 + C

Find the value of C. Also find the mean of the distribution.

Answer 1

Since Σpi = 1

We have C + 2C + 2C + 3C + C2 + 2C² + 7C² + C = 1

i.e., 10C² + 9C – 1 = 0

i.e., (10C – 1)(C + 1) = 0

⇒ C = `1/10`

C = –1

Therefore, the permissible value of C = `1/10`  ...(Why?)

Mean = `sum_("i" = 1)^"n" x_"i""P"_"i"`

= `sum_("i" = 1)^7 x_"i""P"_"i"`

= `1 xx 1/10 + 2 xx 2/10 + 3 xx 2/10 + 4 xx 3/10 + 5(1/10)^2 + 6 xx 2(1/10)^2 + 7(7(1/10)^2 + 1/10)`

= `1/10 + 4/10 + 6/10 + 12/10 + 5/100 + 12/100 + 49/100 + 7/10`

= 3.66