Let C be a set in three - dimensional space and let @ ( C ) be equal to the volume of C , if Chas finite* volume ; otherwise , let Q ( O'; be...

Please help with Probability Space functions. The problem is shown in the attachment. I was struggling in understand the concept and I'll be grateful if you can show me the steps to solutions. Thanks in advance!

6. Let C" be a set in three - dimensional space and let @ ( C ) be equal to the volume of C , if Chas finite*volume ; otherwise , let Q ( O'; be undefined . Find Q ( 0) .( a ) (" = ( ( 2 , 4 , 2) ERS : 0 < < < 2, 0 < 3 < 1 , 0 < < < 3 ).( b ) C = ( ( 2 , 3 , 2) ER 3 : 2 2 + 3 2 + 2 2 2 1 ).7 . For every one - dimensional set C for which the integral exists , Q ( C ) = [of (a ) do , where f ( a ) -Gx ( 1 - 2 ) , 0 < < < 1 , zero elsewhere ; otherwise , let @ ( C") be undefined . Find Q ( C" ) .( a ) (1 = PIER : 1 / 4 < < < 3 / 4)( b ) C 2 = ( 1 / 2}( C ) C3 = PIER : 0 < < < 1018. Suppose the experiment is to choose a real number at randomandom in the interval ( 0 , 1 ) . For any subinterval( a, 6) C ( 0 , 1 ) , it seems reasonable to assign the probability P [ ( a , 6) ] = 6 - a; i.e., the probability ofselecting the point from the subinterval is directly proportional to the length of the subinterval . If thisis the case , choose an appropriate sequence of subintervals to shoe that P [ [a] ] - O for all at ( 0 , 1 )Hint : let ( Chin =I may be a decreasing sequence of events , as in Question 2 , then limn_* too P ( On ) -P ( limn_ too On ) = P (17 = 1 On )`