# Cumulative distribution function

• May 19th 2009, 12:23 AM
greghunter
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.
• May 19th 2009, 12:55 AM
SENTINEL4
Quote:

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

$F(4)=\frac{(4+k)^2}{25}=1$ $\Rightarrow$ $(4+k)^2=25$ $\Rightarrow$ $k^2+8k-9=0$
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...
• May 19th 2009, 01:42 AM
greghunter
Ok, I think I get it.