My Math Forum Probability and Expectation of Logical Propositions

 February 28th, 2012, 08:56 PM #1 Member   Joined: Sep 2009 Posts: 71 Thanks: 0 Probability and Expectation of Logical Propositions Given seven propositions of the form $x_{1} \wedge x_{2} \wedge x_{3}$ in which the variables in each proposition are all different(although variables may be repeated throughout the other seven propositions) and may also be negated. a. what is the probability that a single proposition is true? my attempt: A proposition is true if it has at least one true value. The number of propositions with at least one true = total true/false outcomes - number of propositions with no true values =$2^{3} - 1= 7$ Pr[proposition is true] = $\frac{7}{2^{3}}$ b. What is the expected number of true propositions $X:$ random variable denoting the number of True propositions $X_{i}:$ random variable indicating whether the $i^{th}$ proposition is 1: true or 0: false $X = X_{1} + X_{2} + X_{3} + X_{4} + X_{5} + X_{6} + X_{7} E[x] = 1 * \frac{7}{8} + 2 * \frac{7}{8} + 3 * \frac{7}{8} + 4 * \frac{7}{8} + 5 * \frac{7}{8} + 6 * \frac{7}{8} + 7 * \frac{7}{8} = \frac{7}{8}(1 + 2 + 3 + 4 + 5 + 6 + 7)$ Am I on the right track or am I completely wrong?

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post helloprajna Math Books 0 November 18th, 2012 10:50 PM schezleng Probability and Statistics 7 August 5th, 2011 07:56 PM beatdown123 Applied Math 1 September 8th, 2010 10:20 PM YUNGBuckeye23 Advanced Statistics 6 December 19th, 2009 04:20 PM aoricky21 Number Theory 4 September 22nd, 2007 03:35 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top