I need an explanations for these examples:

A panel has 4 on/off switches. Let x be the random discrete variable representing the number of switches that are on.

a) Create a sample space for the event;

b) Create a probability distribution table for the discrete variable x;

c) Calculate the expected value for x.

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In a research project to determine the relationship between the number of test review problems solved and students' grades for the test, 6 students were randomly chosen and below data was collected

x (number of review problems solved)	y (students grades in %)
10	82
12	85
5	45
9	83
15	87
11	86

a) Draw a scatter plot for the data;

b) Find the equation of the line of best fit. Draw the line of best fit on the scatter plot diagram. Round off the coefficients to one decimal place; show all calculations.

c) Find the coefficient of determination. Write a statement of interpretation for it.