Saint Louis University |
Computer Science 462
|
Dept. of Math & Computer Science |
Topic: Probabilistic Reasoning
Related Reading: Ch. 14
Due:
Monday, 3 May 2010 (in class)
Please make sure you adhere to the policies on academic integrity.
We have a bag of three biased coins, a, b, and c, with probabilities of coming up heads of 20%, 60%, and 80%, respectively. One coin is drawn randomly from the bag (with equal likelihood of drawing each of the three coins), and then the coin is flipped three times to generate the outcomes X1, X2, X3.
Let Hx be a random variable denoting the handedness of a person x, with possible values l for x being left-handed and r for x being right-handed. A popular hypothesis is that left- or right-handedness is inherited by a simple mechanism; that is, perhaps there is a gene Gx, also with values l or r, and actual handedness turns out the same (with some probability s) as the gene that the person possesses. Furthermore, the gene itself is equally likely to be inherited from either of a person's parents, with a small non-zero probability m of a random mutation flipping the handedness.
Consider the following three Bayesian Networks.
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(1) | (2) | (3) |