1: introduction to probebilitypdf - Adobe Acrobat Reader DC X Fiie Edit View Window Help Home Tools introduction to pro... X Sign In I$EEQ:@ W_IW:NO125%'_EIE?f@ @ I}, Export PDF v [2| 322 Introduction to Probability *3 Create PDF V @ 10. LetXandY be i.i.d. EX 0A ,andT:X+Y. p l ) E Edit PDF v (a) Find the conditional GDP of T given X : 3. Be sure to specify where it is zero. Comment (13) Find the conditional PDF fT'XMx), and verify that it is a valid PDF. (c) Find the conditional PDF fxam, and verify that it is a Valid PDF. Combine \"'35 V {'13 Hint: This can be done using Baves' rule without having to know the marginal PDF of [I] Organize Pages v T, by recognizing what the conditional PDF is up to a normalizing constantthen the normalizing constant must be Whatever is needed to make the conditional PDF valid. ' ? Fill Br Sign (d) In Example 8.2.4> we Will show that the marginal PDF ofT is fq-(t) = tsM, for _ ._ t > 0. Give a short alternative proof of this fact, based on the previous parts and Bayes' - Send for Signature rule. -)--- Send Br Track 6-) More Tools Store and share lils in the Document Cloud ,_, ._, \\ . ._, i , Learn More about the Normal distribution. v