Answer to #1

1. 30 20 y 10 0 -2 -1 0 1 2 x Answer to #1 How could you sample deviates from a normal and a lognormal distribution that have opposite dependence? Use inverse transform sampling with the uniform deviate for the lognormal deviate equal to one minus the uniform deviate for the normal. In R, this can be done with the following script: p <- runif(200) x <- qnorm(p, mean=0, sd=1) y <- qlnorm(1 - p, meanlog=1, sdlog=1) plot(x,y) In Excel, similar calculations can be done with this construction: A=RAND() B=NORMINV(A,0,1) C=LOGINV(1-A,1,1)

2. Answer to #2 Why is the concentration generally modeled as a point value in PRA’s? Under what conditions should a distribution be used? It’s usually modeled as a point value because receptors (e.g., individual mink, or duck hunters) experience many independent exposures (fish/invertebrate prey, or meals of duck tissue). In effect, the receptor integrates these many independent exposures over time and so his or her exposure is the average of the concentration distribution. When the number of exposures (meals) is few, then there is less contraction to the mean. In general, the standard deviation of the distribution of means from independent samples taken from a distribution with standard deviation s is s/N where N is the number of samples being averaged.

3. Answer to #3 What are the implications of using a uniform distribution to model an interval range? If the interval range is representing incertitude, then the incertitude is treated as though it is variability. This would confound the two forms of uncertainty, the result would likely be an underestimate of the uncertainty in the quantitative output.