Random Variables and Statistical Analysis
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X and Y are random variables.
What are the marginal pdfs of (x+y) (where 0<x<1 and 0<y<1)?
What is the expectation, covariance, correlation and and covariance coefficient?
What are the joint and marginal pdfs and cdfs?
(ii) Also,differently - if Fx|y(x|y) is constant over the 0 to 1. What is Fy|x(y|x)? (is there enough information to determine this?)
(iii) X and Y are random variables
Z=XY (x and y: X^2+y^2<=1)
What is the cdf, pdf, expectation, and variance?
Thanks. Please answer the first one. The second and third may not have enough information. If not, then please explain the relationship between Fx|y(x|y) and Fy|x(y|x) in ii and how to find the cdf, pdf, etc of Z when Z is a product function of two random variables.
Please provide whatever information you can from the information provided here (on any of the problems). I'm looking for insight.
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Solution Summary
This solution has step-by-step calculations to determine the marginal pdf, expectation, covariance, correlation and covariance coefficient. All formulas and workings are shown.
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"
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