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3. A certain region in the Southeastern United States is hit by an average of 1.7 tropical storms per hurricane season. Assume that tropical storms occur randomly and independently and are typically modeled by a Poisson random variable. The hurricane season is from June 1 through November 30, consisting of 183 days. a. Calculate the probability that the region is hit by at least two tropical storms in more than half of the next 5 hurricane seasons. b. Calculate the probability that there is window of at least 6 weeks (42 days) during a particular hurricane season, in which there are no tropical storms. C. Furthermore, 10% of tropical storms grow into "Hurricane" status. (Note not relevant to the solution of the problem, but a hurricane is defined as a tropical storm with winds 74 mph or greater)- Calculate the probability that in a given hurricane season this region is hit by exactly 3 tropical storms, one of which gets classified as a "Hurricane". 4. Consider Random Variables X and Y with the following joint probability distribution. 0 2 0.3 0.1 0 X NHO 0.1 0.2 0.1 0.1 0.1 a. Determine E(5X + 10Y). b Calculate P(5X + 10Y) 2 20. C. Determine the correlation coefficient, Pxy-5. Each day a Baker bakes multiple loaves of bread. Although the baker strives for consistency, the weight of each loaf varies slightly. Suppose that the weight of a loaf of bread is Normally distributed with a mean of 24 ounces and a standard deviation of 0.8 ounces. Furthermore, assume that weights of loaves of bread are independent a. If one loaf is randomly selected, determine the probability that it weight is less than 23 ounces . b. Determine the value that best completes the following sentence: 15% of the loaves that this baker bakes weigh more than ounces. C. If 10 loaves of bread are pulled off the shelf to fill an order, what's the probability that the total weight (10 loaves combined) is more than 244 ounces? 6. Random variables X" and Y' are defined by the joint probability density function fur ( x, y ) = to x20, y20 otherwise Are X and Y independent? Justify your answer. b. Calculate the probability P(X