Multivariate lognormal distributions
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Similar to the univariate case, bivariate lognormal random variables have a PDF
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for x1, x2 > 0, in which
where pln x and ulnx are the mean and standard deviation of log-transformed random variables, subscripts 1 and 2 indicate the random variables X1 and X2, respectively, and p12 = Corr(ln X1, lnX2) is the correlation coefficient of the two log-transformed random variables. After log-transformation is made, properties of multivariate lognormal random variables follow exactly as for the multivariate normal case. The relationship between the correlation coefficients in the original and log-transformed spaces can be derived using the momentgenerating function (Tung and Yen, 2005, Sec. 4.2) as
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The best way to obtain accurate lengths for cripples and trimmers is to make a story pole. As the name suggests, this straight length of wood (I use a 2×4) tells a story. In this case, it’s the description of a wall layout, with the locations of sills and headers for windows and doors providing the measurements for cutting cripples and trimmers. With a story pole, you do all the measuring once, double-check everything, then use the pole as a reference for the entire layout. Instead of repeatedly measuring cripples and trimmers with a tape measure, you simply transfer the layout marks from the story pole.
