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I need your help to understand this homework.

A weather station recorded every 10 minutes the temperature. X is the minimum and Y the maximum temperature in a day. between the 1st and 30th April the values of X are in [0,15] and the Y are in [10,30] 1) draw the sample space and the following contingencies A={temperature during the day does not exceed 25 degrees} B={maximum temperature of the day is at least twice the minimum} C={the difference in maximum & minimum temperatures of day does not exceed 5 degrees} 3) Are the contingents A and C independent?

My basic problem is that i can’t understand who is the sample space and the A, B and C, i am very confused. At first i think that the sample space is Ω={0≤x≤15, 10≤y≤30} and A={y≤25}, B={y≥2x}, C={(y-x)≤5} but I am sure that isn’t right.

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    You can edit the question using the "edit" link underneath it. Then people don't have to read through all the comments to understand the question.2011-11-04

1 Answers 1

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I think what you've done so far is correct, although I would write it a little bit differently: $\Omega=\lbrace(x,y):0\le x\le15,10\le y\le30\rbrace$ $A=\lbrace(x,y){\rm\ in\ }\Omega:y\le25\rbrace,\quad B=\lbrace(x,y){\rm\ in\ }\Omega:y\ge2x\rbrace,\quad C=\lbrace(x,y){\rm\ in\ }\Omega:y-x\le5\rbrace$