Question

1) The following problems are intended to show how we can use double integral to solve a fundamental problem in Probability and Statis- ties. It is known that we cannot compute the indefinite integral Jede. Recall that to even compute we have to resort to approximation techniques as we cannot get the exact value. As it turns out, we can compute exactly the value dr. a. Argue why the improper integral To dr does converge. Lets give this value a name. I will call it M for magical as we will be able to find out what it is exactly. So dxM b. Explain why the improper integral dr does converge c. True or False dy.

Answer 1

f a ) a a da e X u get let ? D.wor.t. 'x' , we 2x dx du du => da 2 tu Limits da = don't change 4 du 2 seu *ste at du 아 of -1 LL 2 du и e f U n-1 du = Gammar u W.KT function T(m) - sē Ś P6 T est- finite value y 4 :: S म e *** courges b) e da = pter en b ) s o an since e a even function. = Q ) T - finite ale of s .. e da converges. 'of

f * 2 2. N c) da e dy e } 0 TI - 7 뮈 21 12 Ang: Tone