Final answer:
A Monte Carlo algorithm to determine the expected value E[X] involves generating random values of X based on the density function f(X) = Ce⁴⁵ + X² and calculating their average.
Step-by-step explanation:
The subject question asks for a Monte Carlo algorithm to determine the expected value or mean (E[X]) of a random variable X with a given density function f(X) = Ce⁴⁵ + X². To accomplish this, Monte Carlo simulation can be used. In such a simulation, a large number of random values for X are generated according to the probability density function (PDF), and then the mean of these values is computed to estimate E[X]. To ensure the simulation follows the given PDF, one might need to determine the constant C through normalization that makes the integral of the PDF over the range (0,1) equal to 1.