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Year 2 of the mathematics and philosophy course of the University of Oxford

Options I for mathematics and philosophy course of the University of Oxford

Past exam of the options I for mathematics and philosophy course of the University of Oxford

2013

For integer-valued <random variables>, the <joint probability mass function> is
$$
\boxed{p_{X,Y}(x,y)=\mathbb P(X=x,Y=y),\qquad x,y\in\mathbb Z.}
$$
The <marginal probability mass functions> sum out the other variable:
$$
\boxed{p_X(x)=\sum_{y\in\mathbb Z}p_{X,Y}(x,y),\qquad p_Y(y)=\sum_{x\in\mathbb Z}p_{X,Y}(x,y).}
$$
All masses are nonnegative, and their sums over the corresponding sample values equal one.

Solution

Past exam of the options I for mathematics and philosophy course of the University of Oxford / 2013 / N / 1 / a / Solution

Past exam of the options I for mathematics and philosophy course of the University of Oxford / 2013 / N / 1 / a / Solution

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