Question

2. According to genetic theory, there are three blood types MM, NM and NN which should occur in a very large population with probabilities, O, (1-9)3 and 30(1-0), where is the (unknown) gene frequency, 0 s 0S1. (Note: This distribution is for exercise purposes only and may not be true in real life.) (a) Suppose that in a random sample of size n = 10 from the population, there are f, f, and fs of types MM, NM and NN respectively. What distribution can we assume for the frequencies,fi, f2, and fs? Write down its probability mass function. Blood T Total NM f2 Observed frequencyf Probability b) What are the assumptions required for the distribution you assume in part (a)? (c) Write down the Log-likelihood function as a function of θ, 1(9). Write down the Score function, S(0) d) Find an expression for the maximum likelihood estimate of 0 (e) Suppose that fl-3, f2-5, and f,-2. Compute the maximum likelihood estimate of θ (f) Compute the estimated probabilities for Pi, p2 and pa under this model. i.e. p,(0), i 1,2,3. (g) Compute the estimated expected frequencies under this model np,() and compare and them with the observed frequencies. Comment on your findings.

Answer 1

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)052 6+5 6+ 10+ 2 (J) t χ pected frequenaes ase (alcLc.kcí by T observed freaencies ane 2,5, 3