Finding c from probability density function?

probability density function f(x) = cx^2, for x = 0 to 3.


what is c?

Finding c from probability density function?
A probability density function (or probability distribution function) is a function f defined on an interval (a, b) and having the following properties.








(a) f(x) %26gt;= 0 for every x


(b) Integral (from a to b) f(x) dx = 1





this implies:


cx^2 %26gt;=0 for x =0 to 3 ---%26gt; c %26gt; 0 ( c has to be positive)


and


∫ (0 to 3) cx^2 dx = 1


--- %26gt; c ∫ (0 to 3) x^2 dx = 1


----%26gt; c [ (1/3) x^3 ] (from 0 to 3) = 1


-----%26gt; (c/3) [ 3^3 - 0 ] = 1


----%26gt; (c/3) (3^3) = 1


-----%26gt; c = 1/(3^2) = 1/9


Hope this helps
Reply:Simply integrate the function on the interval from 0 to 3:


∫cx²dx = ⅓c[3³ - 0³] = 1


27c = 3, or c = 0.1111....





The sum of the probability density is 1.
Reply:for f to be a pdf it must integrate to 1 over the region





3


∫ f(x) dx =1


0





c/3 * (3 ^3 - 0 ^ 3) = 1





c = 1/9