1. ## Cumulative distribution function

The discrete random variable can only take the values 2, 3, 4. For these values the cumulative distribution function is defined by

F(x)= ((x+k)^2)/25 for x= 2, 3, 4,

where k is a positive integer.

Find k

I know there must be a method for this but I can't find out what it is.

2. Originally Posted by greghunter
The discrete random variable can only take the values 2, 3, 4. For these values the cumulative distribution function is defined by

F(x)= ((x+k)^2)/25 for x= 2, 3, 4,

where k is a positive integer.

Find k

I know there must be a method for this but I can't find out what it is.
Well i'm not sure about that but let's see...

As x can only take values 2,3,4 i suppose that it will be

$\displaystyle F(4)=\frac{(4+k)^2}{25}=1$ $\displaystyle \Rightarrow$ $\displaystyle (4+k)^2=25$ $\displaystyle \Rightarrow$ $\displaystyle k^2+8k-9=0$
The solutions are k=-9 and k=1 but as you say it is a positive integer we accept k=1.

Hope i am right and helped you...

3. Ok, I think I get it.