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cs-677:conjugate-pair-and-functions-of-random-variables [2015/01/06 21:11] (current)
ryancha created
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 +===3.7===
  
 +Problems 3
 +
 +===3.8===
 +
 +Problems 4 <!-- and 11-->
 +
 +===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 ยท Last modified: 2015/01/06 21:11 by ryancha
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