The following table gives the joint probability function y1 3. 1/12 1/9 1/6 1 1/18 2/9 2 y2 1/9 1/6 1/12 3 P (Y < Y2) Find 1/2 O 5/9 11/36 1/4 13/36 5/12 O
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Q: The following table gives the joint probability function y1 3 2 1 1/12 1/9 1/18 1 1/18 2/9 y2 1/9…
A: Solution: From the given information, the joint probability function is
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A: Since the domain (s) is defined pointwise rather than as an interval
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- Suppose a particle moves along tje x-axis beginning at 0. It moves one integer step to the left or right with equal probability. What is the probability function of its position after four steps?The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.2380.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500n=500 of young adults ages 20–39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, ?,X, in Lance's sample who regularly skip breakfast is greater than 126126. You may find table of critical values helpful. Express the result as a decimal precise to three places. Then, Apply the central limit theorem for the binomial distribution to find the probability that the number of individuals in Lance's sample who regularly skip breakfast is less than 9898. Express the result as a decimal precise to three places.The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.2380.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500n=500 of young adults ages 20–39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, ?,X, in Lance's sample who regularly skip breakfast is greater than 126126. You may find table of critical values helpful. Express the result as a decimal precise to three places.
- Let Mx, y be the moment generating function of random variables that are not independent of X and Y. Which of the following / which are not the properties of the function Mx, y?A park ranger is searching for bears in a region of the park where on average there are 5 bears per square mile. The bears are solitary independent creatures, so it is reasonable to assume that the numbers of bears in disjoint regions are independent unknowns and that the number expected in any region is proportional to the area of the region. The ranger can also assume that in a very tiny region, say a square inch, it is impossible to find more than one bear. What is the probability (two decimal place accuracy) that he finds less than 12 bears in a given 2 square mile region of the park?A harried passenger will be several minutes late for a scheduled 10 A.M. flight to NYC. Nevertheless, he might still make the flight, since boarding is always allowed until 10:10 A.M., and boarding is sometimes permitted up to 10:30 AM. Assuming the end time of the boarding interval is uniformly distributed over the above limits, find the probability that the passenger will make his flight, assuming he arrives at the boarding gate at 10:25.
- The amount of time that Alyse has waited for the school bus this year can be modeled by a uniform discrete interval from 0 to 4 minutes. Find the probability that on a randomly selected day Alyse waits less than for 10 minutes for the bus to arriveThe amount of time it takes Alice to make dinner is continuous and uniformly distributed between 10 minutes and 46 minutes. What is the probability that it takes Alice more than 42 minutes to finish making dinner given that it has already taken her more than 32 minutes in the making of her dinner?X and Y are continuous random variables with pdf f(x,y) = 2x for0 ≤x ≤y ≤1, and f(x,y) = 0 otherwise. Find the conditional expectation ofY given X = x.
- A factory received a shipment of 9 flanges, and the vendor who sold the items knows there are 2 flanges in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the flanges in the sample are defective, he will refuse the shipment. Give answer as a decimal to three decimal places. (a) If a sample of 2 flanges is selected, find the probability that all in the sample are defective. 0.99Incorrect (b) If a sample of 2 flanges is selected, find the probability that none in the sample are defective.The amount of time that Alyse has waited for the school bus this year can be modeled by a uniform discrete interval from 0 to 4 minutes. Find the probability that on a randomly selected day Alyse waits less than for 1 minute for the bus to arriveFor a given electronic component, it has been shown that it is necessary to restart once every 250 hours. Let X be the number restarts within 1000 hours. (f) Given that the electronic component has been operating continuously for 200 hours, what is the probability that it will operate for another 400 hours?