Open RStudio. Create a new project (File -> New Project). Select New Directory. Select New Project. Name the directory Lab6. Change the project's path/subdirectory, if necessary. Click the Create Project button. Be sure to use the following to load the tidyverse: library(tidyverse) This lab will use the diamonds sample dataset. This dataset contains information on some 50,000+ diamonds including attributes like price, cut, and carats. For more information, use help("diamonds") in RStudio. After loading the tidyverse with the command above, enter diamonds to display the first few rows of the data frame. > diamonds # A tibble: 53,940 x 10 carat cut color clarity depth table price X y Z 1 0. 23 Ideal SI2 61. 5 55 326 3. 95 3. 98 2.43 2 0. 21 premi um SI1 59. 8 61 326 3. 89 3. 84 2. 31 0. 23 Good VS1 56.9 65 327 4.05 4. 07 2. 31 4 0. 290 Premium VS2 62.4 58 334 4.2 4. 23 2. 63 5 0. 31 Good MIHUUHMmm SI2 63. 3 58 335 4. 34 4. 35 2.75 6 0. 24 very Good VVS2 62. 8 57 336 3.94 3.96 2. 48 7 0. 24 very Good I VVS1 62. 3 57 336 3. 95 3. 98 2.47 8 0. 26 very Good H SI1 61.9 55 337 4. 07 4. 11 2. 53 9 0.22 Fair VS2 65. 1 61 337 3. 87 3.78 2.49 10 0. 23 very Good H VS1 59.4 61 338 4 4. 05 2. 39 # . . . with 53,930 more rows 1. Where X is the price of a diamond, what is the expected value E(X)? 2. Where X is the weight of a diamond (carats), what is the expected value E(X)? 3. Where X is price of an "Ideal" cut diamond, what is the expected value E(X)? What is Var(X)? The standard deviation? Hint: The probability of each Ideal cut observation, P(X = x;), is 1umber of Ideal observations Hint: Running var(Ideal cut prices) will return the estimated population variance. The sample variance (what this question is first asking for) will be close to this. 4. Where X is price of an "Fair" cut diamond, what is the expected value E(X)? What is Var(X)? The standard deviation