Vectors

1. Create a vector containing NA repeated 100 times.

2. Create a vector containing 0 repeated 3 times.

3. Create a vector containing the numbers 0, 0.01, 0.02,…, 3 (the sequence from 0 to 3, incrementing by 0.01).

4. What is the 23rd entry in the vector you created in question 3?

5. Take the square root of all entries of the vector in question 3, using a for loop.

6. Take the square root of all entries of the vector in question 3, without using a for loop.

Random sampling

7. Choose a random sample of 10 integers between 1 and 100, without replacement.

8. Choose a random sample of 10 integers between -2 and 2, with replacement.

9. Sample 1000 observations from a \(N(3, 11)\) distribution (11 is the variance, not the standard deviation).

Functions

10. Write a function with the following specifications:

• Arguments: a sample size n, a slope beta1, and an intercept beta0
• Simulates \((X_1, Y_1),...,(X_n, Y_n)\) with \(X_i \sim N(0, 1)\) and \(Y_i = \beta_0 X_i^{\beta_1}\)
• Returns a plot of \(Y_i\) vs. \(X_i\)

11. Write a function with the following specifications:

• Arguments: a sample size n, a slope beta1, and an intercept beta0
• Simulates \((X_1, Y_1),...,(X_n, Y_n)\) with \(X_i \sim N(0, 1)\) and \(Y_i = \beta_0 X_i^{\beta_1}\)
• Returns a list of length 2, where the first component contains the \(X_i\), and the second component contains the \(Y_i\)

Lists

12. Create a list x such that the vector c(2, 7, 9) can be extracted with x[[2]][[2]].

13. Explain why the following code causes an error:

x <- list(function(n){return(rnorm(n, mean=0, sd=3))},
          function(n){return(runif(n, min=0, max=1))})

x[1](10)

## Error in eval(expr, envir, enclos): attempt to apply non-function

14. Modify the code in question 13 to sample 10 observations from a \(N(0, 9)\) distribution.