At a certain time, the number of people that enter an elevator is a Poisson random variable with parameter λ. The weight of each
person is independent of other person’s weight, and is uniformly distributed between 100 and 200 lbs. Let Xi be the fraction of 100 by which the i th person exceeds 100 lbs, e.g., if the 7th person weighs 175 lbs, then X7 = 0.75. Let Y be the sum of the Xi .(a) Find MY(s).(b) Use MY(s) to find E[Y].(c) Verify your answer to part (b) by using the law of iterated expectations.
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Answer:
Step-by-step explanation:
The formula you wrote has the fraction the other way around. You can find that the range of a projectile is in reality approximated by the equation , where we will use ft for distances.
From the given equation we have then , which means
since the arcsin is the inverse function of the sin.
Since we have x = 170 ft and v = 85 ft/s, we can substitute these values from the equation written, and we will have , and from now on we have just to use a calculator, obtaining