My Math Forum Need some help figure out this normal distribution

 Probability and Statistics Basic Probability and Statistics Math Forum

 December 25th, 2015, 06:39 PM #1 Member   Joined: Apr 2014 From: Birmingham, AL Posts: 36 Thanks: 4 Need some help figure out this normal distribution I am stumped and need someone better at this than me I am trying to find the mean and variance of the following normal random variable: X ~ N(d+eY,a) Y ~ N(b,c) a,b,c,d,e are known constants. I would like to solve for the mean and variance of X. I guess the mean would be d+eb. How could I find the variance?
 January 1st, 2016, 05:57 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 ?? The notation "$\displaystyle N(\mu, \sigma)$" means "the normal distribution with mean $\displaystyle \mu$ and standard distribution $\displaystyle \sigma$. "N(d+ ey, a)" says that the mean is d+ ey and that the standard deviation is a so the variance is $\displaystyle a^2$. (The variance is defined as the square of the standard deviation.)
 January 3rd, 2016, 05:34 PM #3 Member   Joined: Apr 2014 From: Birmingham, AL Posts: 36 Thanks: 4 Hey Country Boy, thanks for the reply and we live in the same state! Yes I do know what this notation means. Maybe I am still not posing the question correctly. I want to know the unconditional distribution of X. X's mean is a linear combination of the random variable Y. I wish I knew how to write formulas.. I know the pdf of X is the integral from -infinity to infinity of 1/(sqrt(2pi)*a)*exp(-(x-y)^2/2a^2)*1/(sqrt(2pi)*c)*exp(-(y-b)^2/2c^2) dy I do not know how to do this integral. I have tried but am stumped.
 January 16th, 2016, 08:18 AM #4 Member   Joined: Apr 2014 From: Birmingham, AL Posts: 36 Thanks: 4 Var(X) = E[Var(X|Y)] + Var(E[X|Y]) = a + c. Don't I feel like an idiot. This is why you should always read your textbook!

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post nakys Advanced Statistics 0 October 3rd, 2013 08:27 AM hoyy1kolko Algebra 1 August 8th, 2011 01:49 AM baxy7 Advanced Statistics 2 August 2nd, 2011 01:06 AM falonsos Advanced Statistics 1 August 17th, 2010 01:11 PM Airin10E Algebra 2 December 17th, 2008 07:12 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top