Acrobat Pro DC File Edit View Sign n Window Help M C 5 2 1 7 : ) 72% [ Mon Nov 2 8:57 PM Q . . . 1.pdf Home Tools 1.pdf ? A T 1 /1 + 66.9% 1. Some people suffer an extreme allergic reaction to insect venom, severe enough to cause anaphylactic shock, and rarely, death if not immediately treated. Suppose that over time, a certain hospital emergency room determines that X = "number of deaths due to insect stings" in the summer is distributed as a Poisson variable, with mean 0.1 cases during the month of June, 0.2 cases during the month of July, and 0.3 cases during the month of August. Use this to each of the following. (Assume mutual independence of deaths over the three months.) SHOW ALL WORK! Note: Express each answer in closed mathematical form before you calculate. (a) What is the expected number of deaths over the entire three months? (3 pts) (b) Determine each of the six cell probabilities below. (12 pts) Months June July August # deaths X=0 X=1 (c) Determine the probability that there are no deaths over the entire three months. (3 pts) (d) List all of the ordered-triple outcomes (X,, X2, X, ) that belong to the event that there is exactly one death over the three months. (3 pts) (e) Determine the probability of this event using each of the following, and show they are equal. (6 pts) part (a) parts (b) and (d) (f) Determine the probability that there are at least two deaths over the three months. (3 pts)