Thankyou so much. I have got the answer to both of ours problems. You are correct, its simply the convolution of the two pdf's. Also for the problem of a^4, the derivation for its pdf is given in the book called : "Probability with Random Processes with Applications to Signal Processing" by Henry Stark and John W. Woods on page 131. Thankyou once again for your response. Nishit Nandan Das <nandan@nand...> wrote:In general, if Z = X + Y and X and Y are independent, then pdf Z is the convolution of the pdfs of X and Y. Is that easy to find for your distributions of chi-sq and GAussian? I don't know..but you can (in theory) find it. Nandan On 3/5/06, Nishit Jain <bignishit@bign...> wrote: Thanks for the reply but not exactly I am looking for that !! I am looking for a case where X is chi square and Y is gaussian distributed and I want the distribution of Z(=X+Y). And my colleague Vimal is looking for a case of X^4 where X is Gaussian. Can you give me some reference where I may find any similar discussion? Nishit Bavithi <bavithi@bavi...> wrote:If X & Y are gaussian distributed, their envolopes are Rayleigh distributed & variance of Z(=X+Y) should be exponential. Is this what you are looking for? On 3/3/06, Nishit Jain <bignishit@bign...> wrote: Hi Vimal and all, I am also dealing with a similar problem, but my problem is slightly different. I have a function of RV (Random Variable) which is sum of squares of the Gaussian RV. In literature I have found that the sum of squares of Gaussian RV is a Chi-Square Distribution. I dont exactly know about the fourth power of Gaussian !!! Now my problem is I have a random variable Z : Z = X + Y, where X = Non-zero mean Chi-Square and Y = non-zero mean Gaussian RV. Now I am wondering, what would be the distribution of Z ? Can anybody help us out in this matter? Thanks and regards, Nishit Vimal <vimal125@vima...> wrote: Dear All, In my work I am using MATLAB function RANDN to generate zero mean and variance 1 random numbers. I know the PDF for this is Gaussian which is well defined in literature and I can find loads of information on it. But in my work I happened to get four different Gaussian numbers multiplied together i.e.: a4 = a*a*a*a (where a is a Complex Gaussian number) I am interested in analyzing the statistics of a4. Can anyone please tell me what would be the PDF of such random numbers i.e. a4. The shape I am getting for PDF from MATLAB looks similar to CHI-SQUARE and RAYLIEGH DISTRIBUTION. But I had a look into CHI-SQUARE and RAYLEIGH distributions and not completely convinced that a4 is CHI-SQUARE or RAYLEIGH distributed. Could someone please help me out here, I would really appreciate it. Thank you.