Numerical Methods in R

Numerical Quadrature

1. Define numerical quadrature.
2. Explain why one might need to use numerical quadrature rather than use an indefinite integral and the Fundamental Theorem of Calculus to find the area under a curve.
3. Use integrate() to evaluate a definite integral.
   • Both proper and improper definite integrals.
4. Find the cumulative distribution function \(F\) of a continuous random variable \(X\) using its probability density function \(f\) and integrate().

Symbolic Differentiation with the Deriv Package

1. Define a symbolic derivative.
2. Use Deriv() to compute the symbolic derivative of a function \(f\) up to some order.
3. Define the \(r\)-th moment of a random variable \(X\).
4. Use a given moment generating function \(M_{X}(t)\) of a random variable \(X\) to find its \(r\)-th moment using Deriv().