[SOLVED] CECS451 Assignment 6

Description

General Instruction

• Submit your work in the Dropbox folder via BeachBoard (Not email or in class).
• Submit the separate files as they are. (no zip file)

1. (10 points) Implement a program to compute π value using Monte Carlo simulation method. Use Python 3 and the name py
   • The program should generate n points to compute π for n ∈ {10³,10⁴,10⁵,10⁶}.
   • You can use pi to compute error rates.
   • Please follow the output format. (Fix precisions using “0:.nf”.format) n = 10 ^ 3 pi = 3.096000 error = 1.4513 % n = 10 ^ 4 pi = 3.136800 error = 0.1526 % n = 10 ^ 5 pi = 3.145280 error = 0.1174 % n = 10 ^ 6 pi = 3.140568 error = 0.0326 %
2. Consider Figure 1, and implement a program to answer the query) by using Gibbs (MCMC) sampling. The program should generate 1,000,000 samples to estimate the probability. Use Python 3 and the name py
   • (8 points) Show
   • (16 points) Show the transition probability matrix Q ∈ R^4×4 where q_ij = transition probability from S_i to S_j in Figure 2.
   • (20 points) Show the probability of the query
   • Please follow the output format. (Fix precisions using “0:.nf”.format)

Part A. The sampling probabilities

P(C|-s,r) = <…, …>

P(C|-s,-r) = <…, …>

P(R|c,-s,w) = <…, …>

P(R|-c,-s,w) = <…, …>

Part B. The transition probability matrix

Part C. The probability for the query

P(C|-s,w) = <…, …>

CECS 451                                       Assignment 6 – Page 2 of 2

Figure 1: A multiply connected network with conditional probability tables

Figure 2: Possible states diagram