N12 an12 S

Here, o2 = a2/2 + S2/4 + <r2. The standard deviations of both Za and Z$ are (approximately) equal to one, and they are independent.

(a) Write a function that simulates the statistic. The input to this function should be the relevant parameters and the number of iterations required.

(b) Plot the distribution of the statistic under the null distribution (a = S = 0) and under various values of the parameters.

(c) Identify the threshold for the test of the null hypothesis that will ensure a significance level of 5%. Compare this threshold determined by simulation with that determined from the chi-square distribution with two degrees of freedom.

(d) Compute the power of the test for various values of the parameters.

4.2. Compare the distribution of the statistic UBC = Z2 for the backcross with the distribution of UIC = Z2a + Z2 for the intercross. You may assume that <r2 is the same for both designs.

(d) Why might the assumption that a^ is the same for both designs fail to be satisfied?

4.3. It can be shown that at a marker having a recombination fraction 6 with the QTL

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