A Calculus Instructor Uses Computer Aided Instruction and Allows Students $$\begin{array} { c c } \text { Students } & \text { Number of Tests } \\\hline 10 & 1 \\7 & 2 \\2 & 3 \\1 & 4\end{array}$$

A calculus instructor uses computer aided instruction and allows students to take the midterm exam as many times as needed until a passing grade is obtained.Following is a record of the number of students in a class of 20 who took the test each number of times. $$\begin{array} { c c } \text { Students } & \text { Number of Tests } \\\hline 10 & 1 \\7 & 2 \\2 & 3 \\1 & 4\end{array}$$
a.Use the relative frequency approach to construct a probability distribution and show that it satisfies the required condition.
b.Find the expected value of the number of tests taken.
c.Compute the variance.
d.Compute the standard deviation.