Two-Way Tables

Key Questions

  • If you are given a pmf = pXY(x,y)

    and you would like to find the marginal pY(y)

    we would use the formula py(y)=ip(xi,y)

    in other words you would sum over all of x at the point y

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    So if we look at this table and want to find the marginal pY(3)

    we go:

    pY(3)=P(Y=3)
    =P(Y=3,X=3)+P(Y=3,X=4)
    =0.1+0.2
    =0.3

    Now to look at the formula for the conditional probability

    we can look at the formula for x given y which is a conditional probability.

    pXY(xy)=P(X=xiY=yj)=P(X=xi,Y=yj)P(Y=yj)

    =pXY(xi,yj)pY(yi)

    now to use an example, we will look back at our table.

    let us look for the conditional probability of:

    pXY(34)=0.10.4=0.25

    Thus, the probability that X=3 given that Y=4 is 0.25

  • A two-way table is a display of data divided into two different categories of subsets.

    In the example below, the categories are
    age range: with subsets for ages 0-5, 6-10, and 11-15
    color preference: with subsets for various color choices

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    The entry at D5 (value 8) indicates that 8 children in the age range 6-10 chose yellow as their preferred color.

    The sum of values across a line indicates the number of children who chose the color for that line across all age ranges.

    The sum of values down a column indicates the number of children surveyed in the corresponding age range.

Questions