This shows you the differences between two versions of the page.

Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||

cs-401r:assignment-2 [2014/09/12 08:51] ringger |
cs-401r:assignment-2 [2014/09/12 08:52] ringger |
||
---|---|---|---|

Line 1: | Line 1: | ||

- | = Bayes Nets = | + | = Probability Theory = |

== Objectives == | == Objectives == | ||

Line 19: | Line 19: | ||

#* Prove that for binary random variables $X$ and $Y$, the event-level independence $(x^0 \bot y^0)$ implies random-variable independence $(X \bot Y)$. Use the usual standard of proof. | #* Prove that for binary random variables $X$ and $Y$, the event-level independence $(x^0 \bot y^0)$ implies random-variable independence $(X \bot Y)$. Use the usual standard of proof. | ||

#* Give a counterexample for nonbinary variables. | #* Give a counterexample for nonbinary variables. | ||

- | # [20 points] Consider how to sample from a categorical distribution over four colors. Think of a spinner with four regions having probabilities $p_red$, $p_green$, $p_yellow$, and $p_blue$. Write pseudo-code for choosing a sample from this distribution. | + | # [20 points] Consider how to sample from a categorical distribution over four colors. Think of a spinner with four regions having probabilities $p_{red}$, $p_{green}$, $p_{yellow}$, and $p_{blue}$. Write pseudo-code for choosing a sample from this distribution. |

# [10 points] Does your pseudo-code scale to a distribution over ten thousand values? If not, rewrite it. If so, say why. | # [10 points] Does your pseudo-code scale to a distribution over ten thousand values? If not, rewrite it. If so, say why. | ||

- | # [20 points] Implement your pseudo-code, run it 100 times, and give the results as a vector of counts over the four colors. | + | # [20 points] Implement your pseudo-code, choose values for the four probabilities on the spinner as parameters to your procedure, and run it 100 times. Give the results as a vector of counts over the four colors. |

# [10 points] Normalize your count vector by 100. How does the result compare with your chosen parameters? | # [10 points] Normalize your count vector by 100. How does the result compare with your chosen parameters? | ||

# [10 points] Compute the mean and variance of the estimated multinomial distribution you just discovered. | # [10 points] Compute the mean and variance of the estimated multinomial distribution you just discovered. |