Question: Climate change appears to affect different parts of the world differently, with increases of precipitation in some parts and decreases of precipitation in others. It also seems to be related to an increase of the frequency of events such as ice storms in some parts of the world...

a) Assume precipitation has increased over 40% of the surface of Earth. What is the probability that among 10 locations randomly sampled at the surface of Earth, four did not experience an increase of precipitation?

b) What is the probability that three out of six locations randomly sampled at the surface of Earth experienced an increase of precipitation, if you know that at least one of the six locations (i.e., you do not know which one) experienced an increase of precipitation?

c) Assume that in a given region, the frequency of ice storms is two per year. What is the probability that there be less than two ice storms in 2 years in this region?

Give at least one reason why the following statements are incorrect. a) If X ~ Bi(n, p), then E(X) = n = Var(X). Answer: .............................. b) If X ~ Po(rn), then P(X 5 1n) = 0.5. Answer: .............................. c) When X is discrete quantitative and Answer: .............................. nonnegative, P(X > 1) = 1 P(X = O). .............................. d) If X ~ N(u, 62 ) , then Answer: .............................. P(Xp520")=0.95 foranyp ando. .............................. e) The distribution X ~ Bi(4, 0.5) is Answer: .............................. symmetrical with respect to 4