Question-83

The joint PMF of two discrete random variables \(X\) and \(Y\) is given by:

\[ f_{XY}( x,y) =\begin{cases} \frac{1}{14}( 2x+3y+1) , & x,y\in \{0,1\}\\ 0, & \text{otherwise} \end{cases} \]

What is the value of \(P( 0< X\leqslant 1\ |\ Y >0)\)? Enter your answer correct to one decimal place.

NoteAnswer

\(0.6\)

NoteSolution

We can build a table of the joint PMF:

\[ \begin{array}{|c|c|c|} \hline & X=0 & X=1\\ \hline Y=0 & \frac{1}{14} & \frac{3}{14}\\ \hline Y=1 & \frac{4}{14} & \frac{6}{14}\\ \hline \end{array} \]

Now:

\[ \begin{aligned} P( Y >0) & =\frac{10}{14} \end{aligned} \] And:

\[ \begin{aligned} P( 0< X\leqslant 1\cap Y >0) & =\frac{6}{14} \end{aligned} \]

Therefore, the required probability is: \(\frac{6}{10} =\frac{3}{5} =0.6\).