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 — cs-677:conjugate-pair-and-functions-of-random-variables [2015/01/06 21:11] (current)ryancha created 2015/01/06 21:11 ryancha created 2015/01/06 21:11 ryancha created Line 1: Line 1: + ===3.7=== + Problems 3 + + ===3.8=== + + Problems 4 + + ===4.1=== + + Problems 6 and 8 + + ===4.2=== + + Problem 8 + + ===4.3=== + + Problems 1 and 6 + + ===4.4=== + + Problem 4 + + ==== Calculating Moments ==== + + $f(x; \alpha, \beta, \gamma) = \begin{cases} c & \mathrm{if}\,​ \alpha < x \le \beta, \\ 2c & \mathrm{if}\,​ \beta < x \le \gamma, \\ 0 & \mathrm{otherwise}. \end{cases}$ + + Calculate $c$ (the constant of integration),​ and then calculate the first, second, and third moments about zero, in terms of $\alpha$, $\beta$, and $\gamma$. + + ===4.6=== + + Problem 5 + + ===4.7=== + + Problem 6 + + ===Poisssson=== + + Assume: + + $x | \theta \sim Poisson(\theta)$ + + # What distribution would make a good (that is, derive the conjugate) prior? Show how you came to this conclusion, that is, do not just look it up. + # Derive the posterior distribution and its parameters in this case. + # Derive the marginal distribution of x. + # Using a prior with $\alpha$ (also called the shape) =5 and $\beta$ (also called the inverse scale) =5 and and data x=5. Compute the posterior. + + ===7.3=== + + Problem 18
cs-677/conjugate-pair-and-functions-of-random-variables.txt · Last modified: 2015/01/06 21:11 by ryancha