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2. Suppose X and Y are the survival times (in days) of two white rats that were subjected to
different levels of radiation. Assume that X and Y are independent, fX(x)={(1+x)21,0,x>0
elsewhere.fY(y)={(1+y)32,0,y>0elsewhere. Show all your work and circle your final answers.
Correct answers with no justifications will not receive any marks. a) Give the joint density of X and
Y. b) Find the probability that the second rat outlives the first rat, P[X<Y].

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