For the discrete random variable X, the probability distribution is given by

Question

P(X=x)= kx x=1,2,3,4,5
=k(10-x) x=6,7,8,9

Find the value of the constant k
E(X)

I am lost , it is the bonus question in my homework on random variables so it must be hard.
Many thanks for any help.

Alicia

Answer 1

graph p
symmetric about x=5 where it is 5k
suspect zero at x = 0 and x = 10 :)
k + 2k + 3k + 4k + 5k + k(10-6)+ k(10-7) + k(10-8) + k(10-9) = 1 if that is the whole distribution

2k + 4k +6k + 8k + 5k = 1
k = 1/25

Answer 2

Thanks a lot. I understood. What is E (X) ?

Answer 3

multiply each x value by its probability (kx)
E(x) is the sum of them all -- the expected value of x.