1. Probability distribution derivation

This is the probability distribution:

p(x) = ax^n , 0<= x <=1

Derive an expression for the constant a, to normalize p(x).

Whats a good starting point for this derivation? My initial thought was to take p(x) = dy/dx, separate variables and integrate using the bounds for x on the right side and then setting a equal to the answer. But I don't think this makes sense. Any suggestions? Thanks,

Kim

2. Originally Posted by Kim Nu
This is the probability distribution:

p(x) = ax^n , 0<= x <=1

Derive an expression for the constant a, to normalize p(x).

Whats a good starting point for this derivation? My initial thought was to take p(x) = dy/dx, separate variables and integrate using the bounds for x on the right side and then setting a equal to the answer. But I don't think this makes sense. Any suggestions? Thanks,

Kim
You need to understand what "normalize" means in this setting. It says that $\displaystyle a$ is such that $\displaystyle p$ is the density of a probability distribution. In other words, it must be such that $\displaystyle \int_{\mathbb{R}} p(x)dx=1$ (the total mass equals 1). Substitute the value of $\displaystyle p(x)$ in this equation (note that $\displaystyle p(x)=0$ is $\displaystyle x\notin[0,1]$), compute the integral, and deduce $\displaystyle a$.

3. Thanks!