Suppose X Gamma(k = 20, = 1). a. What is E(X)? b. Give R commands

Suppose X ∼ Gamma(k = 20, λ = 1).

a. What is E(X)?

b. Give R commands to simulate a sample of 10 observations from the distribution of X.

c. Run the commands in R to generate your data of 10 observations. Using direct calculation, test whether the sample gives evidence against H0 : µ = 25, and find an approximate 95% confidence interval for µ. Verify you get the same results using the inbuilt R command t.test.