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Define a pair of random variables as follows:

$X = \begin{cases} 1 & \text{ if the US dollar value of the Canadian dollar drops next week} \\ 0 & \text{ otherwise} \end{cases}$

$Y = \begin{cases} 1 & \text{if the Bank of Canada raises interest rates next week} \\ 0 & \text{ otherwise} \end{cases}$

An economist estimates the following joint probability function:

$\begin{array}{lc} & \mbox{X } \\ \mbox{Y} & \begin{array}{c|cc} & 0 & 1 \\ \hline 0 & & \\ 1 & & \\ \end{array} \end{array}$

Answer the following questions, rounding your answers to two decimal places where appropriate.

(a) Find the conditional probability function of $Y$ given $X = 1$ :

i. $P(Y=0 | X=1)$

ii. $P(Y=1 | X=1)$

(b) What is the covariance between $X$ and $Y$ ?

(c) Are X and Y independent?

A. No
B. Yes

You can earn partial credit on this problem.