fx-a-x2-for-0-x-2-and-fx0-otherwise-find-the-value-of-a-that-makes-f-a-valid-pdf

Question

Let f(x) = a $$x^2$$ for 0 ≤ x ≤ 2 and f(x)=0 otherwise. Find the value of a that makes f a valid PDF.

Accepted Answer

3/8

Answer

1/2

Answer

3/8 is not acceptable because the function would not be nonnegative on the support in spite of satisfying the integral condition, so no constant exists

Answer

3/4

Let f(x) = a x^2 for 0 ≤ x ≤ 2 and f(x)=0 otherwise. Find the value of a that makes f a valid PDF.