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Bayesian Questions
Bayesian Questions
Which of the following statements are true and false? Prove the true ones and give counterexamples for the false ones. Let X and Z be random variables. (i) If X and Z are uncorrelated, then they are independent. (ii) If X and Z are independent, then E[X2]
Let f be the pdf on a continuous random variable Z. The variance of Z is given by σZ and the pdf is symmetric (f(x) = f(−x)) and everywhere positive. Define another random variable X as X = α3Z3 + α2Z2 + α1Z + α0. (i) For which values of αi are X and Z un
Maximum likelihood estimator
Tumor counts: A cancer laboratory is estimating the rate of tumorigenesis in two strains of mice, A and B. They have tumor count data for 10 mice in strain A and 13 mice in strain B. Type A mice have been well studied, and information from other laborator
Tumor counts: A caTumor counts: A cancer laboratory is estimating the rate of tumorigenesis in two strains of mice, A and B. They have tumor count data for 10 mice in strain A and 13 mice in strain B. Type A mice have been well studied, and information fr
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