OK im prob being really stupid, but i cant for the life of me work out how to do this problem. can someone help???

 

A random variable X takes the integer value x with probability P(X=x) defined by

 

P(X=x) = kx^2, x = 1, 2, 3

P(X=x) = k(7-x)^2 x = 4,5,6

P(X=x) = 0 otherwise

 

Find the value of k

Sum of probabilities should be one.

 

Since you have only 6 possible values for x the equation you have to solve is :

 

k + 4k + 9k + k(7 - 4)^2 + k(7 - 5)^2 + k(7 - 6)^2 = 1

which would be

28k = 1, making k = 1/28

 

Mandrake

Beat me to it

 

Works for continuous as well as discrete stuff, except you have to use integration to find the probability density.

Or discrete with infinite (but countable) values, needing infinite sums.

 

Mandrake

Thank you sir may I

I am dire need of some assistance in understanding predicting probabilities, I am just lost with most of this

What do you find difficult about them?