A mail-order company sends an offer to its population of customers. For a randomly chosen customer, let $B_1$ be 0 if the customer does not buy anything, and 1 if the customer does buy something following the offer. Later, the company sends out a second offer to its customers, and let $B_2$ be analogous to $B_1$ for the second offer. The joint probability distribution for the variables $B_1$ and $B_2$ is as given in the following table:

$$\begin{array}{rc} & B_2 \\ B_1 & \begin{array}{r|rr} & 0 & 1 \\ \hline 0 & & \\ 1 & & \\ \end{array} \end{array}$$

Provide answers to the following to two decimal places.

Part a) Find the expectation of $B_1$.


Part b) Find the variance of $B_2$.


Part c) Find the covariance between $B_1$ and $B_2$.


Part d) Find the variance of the total number of purchases of a randomly selected customer following the two offers.