Problem 2. The 451 houses are roughly classified by the number of bedrooms X and

Question

Problem 2. The 451 houses are roughly classified by the number of bedrooms X and property assessments Y as follows Assessment Y mber of bedroom X (6,700-73,000) (73,000-170,000] (70,000-1, M00,000 median 49,000 median 118,000 median 225,000 a) what is the probability of getting each of the 12 possible combinations of bedroom and assessment? That is, tabulate the joint probability distribution p(x,y). b) Calculate p(x) and p(y) c) Are X and Y independent? d) Calculate correlation between X and Y. When you get mean of y, use the nedian not the interval.

Explanation / Answer

The table shows the probabilities for various mix

b)

p(y):

Take any pair say

(x,y) = (2,49000)

P(x=2) P(y=49000) =

0.030826 not equal to P(2,49000)

Hence not independent.

y 49000 118000 225000 Total x 2 0.044346 0.073171 0.004435 0.121951 3 0.124169 0.312639 0.099778 0.536585 4 0.068736 0.097561 0.126386 0.292683 5 0.015521 0.015521 0.017738 0.04878 Total 0.252772 0.498891 0.248337 1

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