1 a. Suppose that I am interested in the number of mutations at ONE fixed location for 100 patients. Let X-"#patients with mutation" be the random variable. The size of this random variable is 100 1 b. Suppose that I know somehow that the probability of mutation at that position is 0.001. The probability of success of X is 1 c. Suppose that I OBSERVE that 1 out of 100 patients showed mutation. So. X-1 happened. Based on this one observation, use a formula taught in class to get the MLE of probability of success. The mle of p is . (Write it as a decimal, not a fraction) 1d. Next, suppose that I am interested in the number of mutations at 10 locations for 100 patients. I somehow know that the probability of mutation is the same at all the 10 locations. I have the following observation vector. X-go,0,0.0,0,0,0,0.0,1) Here X[ 1 ] is the number of patients with mutation at Position 1, X[ 2 ] is the same for Position 2, and so on. Using this observation vector, find an MLE of p. The MLE of p using the new observation vector is le. The position number which showed one patient out of 100 had a mutation is . (Hint: It is a number between 1 and 10, assuming the positions are numbered 1 through 10.)