Let S be a sample space and E and F be events associated with S. Suppose that Pr(E) = 0.5, Pr(F) = 0.3 and Pr(ENF) = 0.2. Calculate the following probabilities.(a) Pr(E|F)(b) Pr(F|E)(c) Pr(티F')(d) Pr (E'JF')...(a) To find Pr(E|F), simplify the fraction with Pr(EnF) in the numerator andPr(F)in the denominator.Pr(E|F) = || |(Type an integer or a simplified fraction.)

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Answered: Let S be a sample space and E and F be…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A certain mutual fund invests in both U.S. and foreign markets. Let x a random variable that represents the monthly percentage return for the fund. Assume x has mean u = 1.9% and standard deviation o = 0.3%. (a) The fund has over 175 stocks that combine together to give the overall monthly percentage return x. We can consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all world stocks. Then we see that the overall monthly return x for the fund is itself an average return computed using all 175 stocks in the fund. Why would this indicate that x has an approximately normal distribution? Explain. Hint: See the discussion after Theorem 6.2. The random variable -Select-v is a mean of a sample size n = 175. By the -Select- v, the -Select- distribution is approximately normal. (b) After 6 months, what is the probability that thẹ average monthly percentage return x will be between 1% and 2%? Hint: See Theorem 6.1, and assume that x has…
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Let X be a normal random variable with = 9 and o 1.85 and Y be a normal random variable with u = 3 and o 0.45. Assume X and Y are independent. Find the following probabilities: (a) P(X 8, Y 3.75) (d) P(X < 12, 2.1 ≤Y ≤ 3.8)
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Calculate the following probabilities in two decimal places: (a) Y is distributed x 1. Then, Pr( Y>9.49) = (b) Y is distributed to. Then, Pr( Y> -0.5) = (c) Y is distributed F4,- Then, Pr( Y 696 or Y<304) =
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