SOLUTION: Let the function f(x)={cx^2 0 < x < 3 and 0 otherwise 1. Find c. 2. Find the distribution function F(x). 3. Compute F(1 < x < 3).

Algebra ->  Probability-and-statistics -> SOLUTION: Let the function f(x)={cx^2 0 < x < 3 and 0 otherwise 1. Find c. 2. Find the distribution function F(x). 3. Compute F(1 < x < 3).      Log On


   

Question 344362: Let the function f(x)={cx^2 0 < x < 3 and 0 otherwise
1. Find c.
2. Find the distribution function F(x).
3. Compute F(1 < x < 3).
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.+int%28+cx%5E2%2C+dx%2C+-infinity%2C+infinity+%29=1+
+int%28+cx%5E2%2C+dx%2C+0%2C+3%29=1+
%28c%2F3%29x%5E3 evaluated between x=0 and x=3
%28c%2F3%29%2827%5E3-0%5E3%29=1
c=1%2F9
.
.
.
2.F%28x%29=%28cx%5E3%29%2F3=x%5E3%2F27
3. F%283%29-F%281%29=27%2F27-1%2F27=26%2F27