Question

Determine the value c so that each of the following functions can serve as a probability distribution of the discrete random variable X: (b) f(x) = c (2 ) (3 )

( assume 2 & x in same parentheses and 3&3-x) ( x ) (3 - x) , for x = 0, 1, 2

Answer 1

Given the function $f(x)=c*(x)*(3-x)$ and $x=0,1,2$ ,values for the function of these values are determined by substituting the $x's$ in the function $f(x)$ as shown below,

$f(0)=c*(0)*(3-0)=0, f(1)=c*(1)*(3-1)=2c, f(2)=c*(2)(3-2)=2c.$

For it to be a probability distribution, it must satisfy the condition, $summation(f(x))=1, \forall x$

so,

0+2c+2c=1

4c=1

c=1/4

Therefore, a constant c=1/4, makes this function a probability distribution.