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 Advanced Statistics Advanced Probability and Statistics Math Forum

 September 21st, 2018, 03:36 PM #1 Senior Member   Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 Probability Questions Let A be the sample space with six elements A = { a, b, c, d, e, f }. Let P be the probability distribution P(a) = 0.05 P(b) = 0.1 P(c) = 0.05 P(d) = 0.1 P(e) = 0.3 P(f) = 0.4 Consider the events X = {a, b, c}, Y = {b, d, e}, Z = {b, e, f} Evaluate the following: Are the following answers correct?? 1. P(X) = 0.05 + 0.1 + 0.05 = 0.2 2. P(Y) = 0.1 + 0.1 + 0.3 = 0.5 3. P(Z) = 0.1 + 0.3 + 0.4 = 0.8 4. P(X,Y) = P(X and Y) = P({b}) = 0.1 5. P(X|Y) = P(X and Y) / P(Y) = 0.1 / 0.5 = 0.2 September 21st, 2018, 05:34 PM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,373 Thanks: 1275 [QUOTE=zollen;599403] Are the following answers correct?? yes Thanks from zollen September 22nd, 2018, 06:56 AM #3 Senior Member   Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 6. P(Y|X,Z) = P(X,Z|Y)*P(Y)/P(X,Z) = P(X|Y) * P(Z|Y) * P(Y) / P(X,Z) Since P(X|Y) = 0.2 P(Z|Y) = P(Z and Y) / P(Y) = 0.8 P(Y) = 0.5 P(X,Z) = P(X and Z) = P({b}) = 0.1 Therefore P(Y|X,Z) = 0.2 * 0.8 * 0.5 / 0.1 = 0.8 Am I correct? Tags probability, questions Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post zdesignzi9250 Advanced Statistics 4 September 1st, 2014 12:44 PM neilduggan Advanced Statistics 1 November 9th, 2013 11:11 AM jabelone Advanced Statistics 3 April 27th, 2013 12:43 AM sneaky Probability and Statistics 0 September 24th, 2010 09:14 AM jhon13 Advanced Statistics 0 December 31st, 1969 04:00 PM

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