# Math Help - Statistics - PDF functions

1. ## Statistics - PDF functions

wow my book is terrible and doesn't mention these types of problems...just assigns them.

find the constant c for to make the following pdf function.
a. f(x) = cx where x = 1, 2, ... , 25.
b. f(x) = c(x+1)^3 where x = 0,1,2
c. f(x) = c(1/3)^x where x= 1, 2, 3, ...

i know what its asking for but i have absolutely no idea where to begin solving for c.

2. For the first function, you can input each of the values from 1 to 25 and your probabilities must sum to 1. This means that $f(1) + f(2) + ... + f(24) + f(25) = 1$. But $f(x) = cx$ so $c + 2c + ... + 24c + 25c = 1$, or $(1 + 2 + ... + 24 + 25)c = 1$. Hence, you must calculate the sum of the numbers from 1 to 25, which is equal to $\frac{25(1 + 25)}{2}$.