Answer 1 to 5 as much as you can:

1) Sickle Cell Anemia is a genetic disorder that causes the red blood cells to become misshapen and break down. The disorder causes pain, swelling in the extremities, increased risk of infection, and a shorten lifespan. SCA is caused by 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 having just one mutated gene help fight against malaria. Let II = 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 specifically referring to people of African descent. 1 if gene is abnormal H = P(G = 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 Followmg the steps in A E, you ll estimate it usmg 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 it. Assume people \"pair up\" independently of gene status. (Note that p here is population proportion, not a sample proportion as it is in the notes.) B) For a random sample of it people, what is the probability (in terms of p) that 31 have SCA? That is, find P(Y=y|p,n)whereY=X1+X2+...+Xn B) For a random sample of n people, what is the probability (in terms of p) that y have SCA? That is, find P(Y = y lp,n) where Y = X1 + X2 + ... + Xn C) Rewrite your answer in part B) using it instead of p: P(Y = y | n, n) D) Find it, the maximum likelihood estimator (MLE) for it using the sample of n people with y having SCA. E) Write it as a function of p, then replace it with it and p with p = y . What do you notice