# Solve your work in R studio:

1. Generate a random sample of size 24 from the normal distribution with mean 3 and standard deviation 1. Construct a 6 by 4 matrix M from this data vector so that the data fills the matrix in row order. Write single expressions to do each of the following. Print the result, if needed for checking, in a separate expression. (a) How many elements in this matrix are greater than 3? (b) Extract the elements that are greater than 3 in the matrix. (c) Make a copy of the original matrix M, name it M1. Then set the elements that are greater than 3 to zero in N. (d) Make a copy of the original matrix M, name it M2. Then set the elements that are greater than 3 in row 2 and 4 to -5 in M2. (e) Append the vector (1, 2, 3, 4, 5, 6) to the left hand side of the matrix M2. Call the result M3.

2. Use the subscripting operations on state.x77 data matrix to: (a) Find the state with the maximum area (variable Area) in the Mountain region as defined by the factor state.division. Get the state name of the result. (Hint: use help(state) function to read the information about state.x77, state.division, and state.name). (b) Find the average illiteracy rate (variable Illiteracy) in the Middle Atlantic region as defined by the factor state.division. (c) Find the states that have murder rates (variable Murder) less than the first quartile (25%). Get the state names of the result.

3. Diamonds are forever. library(tidyverse) data(diamonds) # Use subscription operations to answer the questions below: (a) What proportion of diamonds are between .50 and 1.5 carats? (b) How many of the diamonds have equal x and z dimensions? (c) How many of the diamonds have a depth more than the mean? (d) How many diamonds have a cut of level `Very Good` or better? Note that cut is an ordered factor, so the levels are in order. (e) Which diamond has the highest price per carat (ppc = price/carat)? What is the value? (f) Find the 95th percentile for diamond price. Try the `quantile()` function. (g) What proportion of the diamonds with a price above the 95th percentile have the color `D` or `J`? (conditional proportion) (h) What proportion of diamonds with a clarity of VS2 have a Fair cut and a table below 56.1? (conditional proportion)

(i) What is the average price per carat (ppc) for Fair cut?