Answer the question A to E as much as you can.

a person inheriting two abnormal genes in chromosome 11 from their parents. If only one of the genes in chromosome 11 is abnormal, the disease isn't present (known as a homozygous or recessive trait, like blue eyes, but worse). The mutation is believed to have originated in Africa, as havingjust one mutated gene help fight against malaria. Let 1: = the probability the gene in chromosome 11 causes SCA in people of African descent. You can assume in the rest of this question that we are specically referring to people of African descent. 1 if gene is abnormal "5 = P0: = 1) where G = {0 if gene is not abnormal Without using gene mapping, the type of gene, G, is considered a latent variable: We can't look at each gene individually and record if it contributes to SCA. Instead, we have to look at the observed variable: disorder status, X. 1 if SCA is present . . _ , . . . = Following the steps In A E, you ll estimate 11' using the observed variable, X {0 if SCA is not present A) Write p = P(X = 1) = the probability someone chosen at random has SCA, as a function of II. Assume people \"pair up\" independently of gene status. (Note that 39 here is population proportion, not a sample proportion as it is in the notes.) B) For a random sample of 7: people, what is the probability (in terms of 39) that 3/ have SCA? That is, find PCY=yIp.n)whereY=X1+X2+...+Xn C) Rewrite your answer in part B) using 1: instead of 3): PO' = y | 11', n) D) Find it, the maximum likelihood estimator (MLE) for 1: using the sample of 7: people with 3/ having SCA. E) Write It as a function of p, then replace n: with ft and p with )3 = 37/31 . What do you notice