1. The problem is to find the moments of a function or distribution, which are measures of its shape and spread. 2. The $n$th moment about the origin is defined as $$\mu'_n = E[X^n] = \int x^n f(x) \, dx$$ for a continuous random variable with density $f(x)$, or $$\mu'_n = \sum x^n P(X=x)$$ for a discrete variable. 3. The $n$th central moment is $$\mu_n = E[(X - \mu)^n]$$ where $\mu = E[X]$ is the mean. 4. Moments help describe characteristics like mean ($n=1$), variance ($n=2$), skewness ($n=3$), and kurtosis ($n=4$). 5. To calculate, identify the function or distribution, then compute the integral or sum for the desired $n$. 6. For example, the first moment (mean) is $$\mu = E[X] = \int x f(x) \, dx$$. 7. The second central moment (variance) is $$\sigma^2 = E[(X - \mu)^2] = \int (x - \mu)^2 f(x) \, dx$$. 8. These formulas allow you to find moments step-by-step by substituting the function and evaluating.