N. Solutions for John E. Freund 'N. If the probability density of xChatePTN. Try Ace AI STEM Tutor by Nunumerade.com/questions/if-the-probability-density-of-x-is-given-by-fxleftbeginarrayll-frack-x312-x6-text-for-x0-0-text-else/GoogleImported From Sa ...N. Handout 4 Exercis.N. Solutions for Finan....All BookmarksNumeradeSearch for answers and textbooksTextbooksAce - Al TutorAsk our EducatorsStudy ToolsStep 1 / 2First, we need to find the cumulative distribution function (CDF) of X. The CDF is given by: F(x)=∫0^x f(t) d t=∫0^x(k t^3)/((1+2 t)^6) d tNow, let's find the CDF of Y. We have Y=(2 X)/(1+2 X), so X=(Y)/(2-Y). Then, the CDF of Y is given by; G(y)=P(Y ≤ y)=P((2 X)/(1+2 X)≤ y)=P(X ≤(y)/(2-y))=F((y)/(2-y))Now, we can find the probability density function (PDF) of Y by differentiating the CDF of Y with respect to y : g((y)/(2-y))Using the chain rule, we have: g(y)=(k((y)/(2-y))^3)/((1+2((y)/(2-y)))^6)·(2)/((2-y)^2)(7) Functions of Random Varia.7.0 Functions of Random Varia...Problem 1 AProblem 1BNow, we can simplify the expression for g(y);Answer g(y)=(2 k y^3)/((2-y)^5)Since g(y) is the PDF of Y, it must integrate to 1 over its domain:Problem 1 CProblem 1DProblem 1EProblem 1 FProblem 1G