There are two routes to get from the student dorms to class - a long route,...

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There are two routes to get from the student dorms to class - along route, which is scenic, and a short route, which is notscenic. You want to study whether the route that the studentschoose to take is independent of the weather (in the context of thetable, this will mean whether X and Y are independent), and yougenerate the accompanying table of probabilities.
Rainy
(Y=0)
Sunny
(Y =1)
Total
Long (X=0) 0.1 0.3 0.4
Short (X=1) 0.2 0.4 0.6
Total 0.3 0.7 1
Calculate E(X) and E(Y ).
(b) Calculate E(X | Y = 0). How is this different from E(X)?
(c) Are the route picked and the weather independent of eachother? Why or why not? Use the numbers from the table to arrive atthe answer.

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Solutionwe are given following table of Joint probabilities and marginalprobabilities of X Route picked and Y WeatherRainySunnyTotalY0Y 1Long X00103PX0 See Answer

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	Rainy (Y=0)	Sunny (Y =1)	Total
Long (X=0)	0.1	0.3	0.4
Short (X=1)	0.2	0.4	0.6
Total	0.3	0.7	1