I need the step by step answers to the following assignment.

MTH 243 Spring 2020 Exam 1 At a community college, a survey of twenty-four freshmen yielded the data shown in the table on the next page. We define three variables on the population of those twenty-four freshmen. Variable is a student's grade point average. Variable is the number of years since a student graduated from high school. Variable is whether or not a student is seeking a degree at the college. Answer the following questions based on the given data. 1a. (10 points) Construct a table that shows the frequencies and relative frequencies of the classes {2.5 1) (3 points) ( 3.5 | 2 and = Yes) 3. (10 points) Are the events { 3.5} and { 2} independent? 4. We randomly select two students in a row with replacement, and we observe the value of the variable on each selected student. The values of will be denoted by 0 (for None), 1 (for One), 2 (for Two), and 3 (for Three). With this notation, each outcome of the experiment is a pair (1 , 2 ) where each can be any of the values 0, 1, 2 or 3. a. (20 points) Construct a table that shows each possible outcome (1 , 2 ) with the corresponding probability (1 , 2 ). b. (20 points) Find the mean and standard deviation of the average value = (1 + 2 )2 defined on the sample space of all samples (1 , 2 ) with their probabilities (1 , 2 ). 5. (20 points) We randomly select three students in a row without replacement, and we observe the value of variable on each selected student. The values of will be denoted by (for Yes) and (for No). With this notation, each outcome of the experiment is a triple (1 , 2 , 3 ) where each can be any of the values or . Construct a table that shows each possible outcome (1 , 2 , 3 ) with the corresponding probability (1 , 2 , 3 ). Table 1: Survey of freshmen Student Grade point number average 1 3.5 3 3.1 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Years since high school None One Two 3.3 3.4 3.0 3.7 2.8 4.0 3.7 3.4 2.9 3.4 3.3 2.6 3.5 3.6 3.7 4.0 3.2 No 3.5 Yes 3.8 2.6 Three 2.7 2.9 Degree seeking