Hi people. I have been given few math problem to solve until middle next week and I haven't been able to solve it so far. I hope that you guys can help me out. I have about 7 questions which i have been able to solve some of it but stil stuck with most part of it. Here is one of the questions: CONSIDER THE CONTINUOUS RANDOM VARIABLE X WITH P.D.F GIVEN BY: f(x) = C/(x+1)^v+1 (x_> 0) where v is strictly positive and C is constant.a) find the value of the constant C. Explain why the p.d.f. does not exist for v=0b)Integrating by parts, find an expression for E(X), stating for what values of vit is defined.There is also question c and d but will keep it out for now. I hope someone can provide me full solution to the above problems without asking paul or martinage direct. Please feel free to email me direct on: amali@blueyonder.co.uk for any help you could give on the above. thnksI

a) Use the fact that integrating the PDF from x=0->Infinity must equal 1. That is, x must take some value between 0 and Infinity (I'm assuming x is non-negative here - if not, the function isn't a PDF for all +ve values of v).

Hi mghiggins. thanks for the reply. I was roughly aware that the sum of the pdf for a positive value of x must equal to 1, but I am looking a rigour integration of the pdf and solve or find a solution for the constant C. In addition. I would also like to prove why the pdf does not exist for v = 0. finaly how to find an expression for E(X). I would appreciate if you could take the time to give me a hand on this. cheers.

The integral with respect to x of C/(1+x)^(v+1) is -C/[v*(1+x)^v]. At x=0 the value is -C/v. As x goes to infinity, the integral goes to zero if v>0. Therefore the definite integral from 0 to infinity is C/v. I hope that's enough to get you started.

Dear Amron,but inmy opinion, you forget the constant 1, so the integral should have an additional x, which will go to infinity when x go to infinity.

Which 1 bothers you?If you prefer, make the transformations z = 1+x and w=1+v and rewrite the problem as the integral from z=1 to z=infinity of C/z^w. Now I hope you agree the integral is -C/[(w-1)*z^(w-1)]. Now we need w>1. At z=1, the integral is -C/(w-1). At infinity it's zero.

Dear Aaron, I am not bothering the 1 with x, but for the 1 at the end of equation. f(x) = C/(x+1)^v+1 (x_> 0) ,the first 1 can be easily solved by your method, but how the second 1,the interagral of it should be x.

Thanks very much for your time Aaron. Would you be kind and have a go at the last part of the question: INTERGRATING BY PARTS, FIND AN EXPRESSION FOR E(X), STATING FOR WHAT VALUES OF V IT IS DEFINED. FINALY: IF A RANDOM VARIABLE Y IS DEFINED BY: Y = 1/(1+X) FIND THE P.D..F OF Y. THANKS V MUCH FOR YOUR TIME.

I think getting more help than what is already given would be a bit like cheeting on your hand-in problems, don't you?Get together with a friend, read a book, take the advice and I'm sure you will be able to solve it.

QuoteOriginally posted by: xmulh2Dear Aaron, I am not bothering the 1 with x, but for the 1 at the end of equation. f(x) = C/(x+1)^v+1 (x_> 0) ,the first 1 can be easily solved by your method, but how the second 1,the interagral of it should be x.I see. You are reading this as:[C/(x+1)^v] + 1while I guess that amali meant:C/[(x+1)^(v+1)]Your interpretation follows the normal precedence of operators rule.I will go one more step with helping amali, but if this doesn't do it you may need to drop the class or get some extra help. E(X) is defined as the integral over the range of X*pdf(X)dx. We know the pdf is v/[(x+1)^(v+1)] and the range is zero to infinity. So we have to integrate vx/[(x+1)^(v+1)]dx. Your professor has kindly suggested integration by parts. Clearly you want to differentiate the x to get 1 and integrate the v/[(x+1)^(v+1)] because you already know how to do this.The integral of UdW equals U*W - the integral of WdU. Let U = x and dW = v/[(x+1)^(v+1)]dx. First, solve for W. Next evaluate x*W at x=0 and x=infinity. Then compute the integral of Wdx and evaluate it at x=0 and x=infinity. Add and subtract these four answers appropriately and you will get the right answer.For the last problem, if y=1/(1+x), you must rewrite C/[(x+1)^(v+1)] using only C, y and v; no x.