Could F Be a Probability Density Function?

f(1) = C(x2 − x4/4) = 3C/4. If C < 0 then this is negative and thats not okay. So no, this cannot be a probability density function.

How do you verify that f is a probability density function?

Solution: To be a valid probability density function, all values of f(x) must be positive, and the area beneath f(x) must equal one. The first condition is met by restricting a and x to positive numbers. To meet the second condition, the integral of f(x) from one to ten must equal 1.

Is f/x a probability density function Why?

The function fX(x) gives us the probability density at point x. It is the limit of the probability of the interval (x,x+Δ] divided by the length of the interval as the length of the interval goes to 0.