Question

For the acceptance-rejection method, please prove that the returned random sample is from the target density \(f(x)\):

A. Discuss the acceptance-rejection method in probability sampling.
B. Prove the validity of the returned random sample from \(f(x)\).
C. Analyze the role of acceptance and rejection criteria.
D. Discuss the efficiency of the acceptance-rejection method.

Answer 1

The random variables X and X represent the generated and accepted samples from the target density function. The acceptance-rejection method requires using the target density function and the proposal density function. This method does not involve constructing confidence intervals.

Step-by-step explanation:

b. Define the random variables X and X in words.

The random variable X represents the generated random sample from the target density function f(x). The random variable X represents the accepted samples from the target density function f(x).

c. Which distribution should you use for this problem? Explain your choice.

To analyze the acceptance-rejection method, we need to use two probability distributions. The first distribution is the target density function f(x), from which we want to generate random samples. The second distribution is the proposal density function g(x), from which we sample to decide whether to accept or reject the generated sample.

d. Construct a 90 percent confidence interval for the population mean number of letters campers send home.

Since this question is about acceptance-rejection sampling, it does not directly concern constructing a confidence interval.