If X and Y are independent, then the conditional expectation of Y. given X is equivalent to: E(Y|X)
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A: The conditional expectation of V(Y | X=x) is given by the following formula.
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Q: 1. If the joint probability is given by: x+ y f(x, y) = 30 for r = 0,1,2, 3; y = 0, 1, 2, Find: (a)…
A: As per our guidelines,we are allowed to answer first three sub-parts only. Thanks a) P(X≤2,Y=1) =…
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A: The problem is solved using the concept of covariance. please find step by step solution below:
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A: Given, We have to find b. Also, find the b when it belongs to S9.
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A: Given,f(x)=e-x ; x>0
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A: From the provided information, Probabilities y = 1 y = 2 x = 1 0.1 0.3 x = 2…
Q: 1. If the joint probability is given by: x + y 30 f(r, y) = for r = 0, 1,2, 3; y = 0, 1, 2, Find:…
A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…
Q: 1. If the joint probability is given by: x + y f(x, y) = 30 for a = 0, 1,2, 3; y = 0, 1,2, Find: (a)…
A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…
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Q: X be a random variable with the followi Value x of X P(X=x) 0.05 10 0.05 20 0.20 30 0.05 40 0.65…
A: x 0 10 20 30 40 P(X=x) 0.05 0.05 0.20 0.05 0.65
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Q: 1. If the joint probability is given by: x+ y f(r, y) = 30 for r = 0, 1, 2, 3; y = 0, 1, 2, Find:…
A: As per our Guidelines we are suppose to answer only one question1)
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Q: 1. If the joint probability is given by: r+ y f(x, y) = for x = 0, 1, 2, 3; y = 0, 1,2, 30 Find: (a)…
A: I solved exactly first three subparts because of bartleby policy if you want more please uplode…
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- Calculate the conditional expectation of Y when X = 2. E(YX2)1. If there are n random variables such that each expectation exist then prove that E(X1+…….+Xn ) = E(X1)+……..+E(Xn). Assume discrete.Possible values of X, the number of components in a system submitted for repair that must be replaced, are 1, 2, 3, and 4 with corresponding probabilities 0.05, 0.05, 0.45, and 0.45, respectively. (a) Calculate E(X) and then E(5 − X). E(X) = E(5 − X) = (b) Would the repair facility be better off charging a flat fee of $110 or else the amount $ 150 (5 − X) ? Note: It is not generally true that E c Y = c E(Y) . The repair facility be better off charging a flat fee of $110 because E 150 (5 − X) =
- Suppose that f (x) = e^-x for 0<x. Determine the following probabilities:The lifespan X (years) of a species of pig has pdff (x) = 3x2e−x^3 , 0 < x < ∞.What is the probability that a pig will live at least 1 year? Given that it lives 1 year, what is the conditionalprobability that it will live for at least another year?Suppose that you inherit $10,000. The will states how you must invest the money. Some (or all) of the money must be invested in stocks and bonds. The requirements are that at least $2000 be invested in bonds, with expected returns of $0.080 per dollar, and at least $1000 be invested in stocks, with expected returns of $0.13 per dollar. Because the stocks are medium risk, the final stipulation requires that the investment in bonds should never be less than the investment in stocks. How should the money be invested so as to maximize your expected returns? To maximize the expected returns, invest$ in bonds and $ in stocks.
- A city uses three pumps to carry water from a river to a reservoir. Pumps A and B are new, and have a probability of failing of 0.015 on any day. Pump C is older, and has a probability of failure of 0.08 on any day. Pumps A and B operate Monday-Friday. On Saturday, pumps A and C operate while pump B is serviced. On Sunday, pumps B and C operate while pump A is serviced. Answer the following questions, assuming that the pumps operate independently of one another, and independently from day to day. Determine the probability that pump A works on a day that it is in use. Find the probability that pumps A and B both fail on a day they are both in use. Compute the probability that at least one pump fails on any Sunday. Find the probability that pump A works, and C fails on any Saturday. Determine the probability that no pumps fail in a week.Let X1, X2, . . . are independent indicator variables with different probabilities of success. That is, P(Xi = 1) = pi. Define Yn = X1 + X2 + . . . + Xn. Find E(Yn), V ar(Yn) and coefficient of variation of Yn1. Find the probability that the circuit operates. 2. It is known that the circuit is operating, find the probability that device A is functional.
- Suppose that spot and futures prices of the underlying asset when hedge is initiated are $3.10 and $2.50 respectively, and when hedge is closed out are $2.90 and $2.80 respectively. 1. What is the meaning of above numbers? 2. What is the basis risk when hedge is initiated? 3. What is the basis risk when hedge is closed out? 4. Is it a perfect hedge? 5. What will be the effective price received (paid) for the hedging asset? (S₂ + F₁-F₂3.) Suppose X has probability generating function GX(t) = 0.2 + 0.3t + 0.1t2 + 0.4t3. What is P(X = 2)? What is P(X = 0)?Suppose that speeding imposes externalities on other people resulting in a social cost of $50. A town is considering hiring an extra police officer to give out speeding tickets. If we want to maximize social welfare (absent enforcement costs), which of the following statements are true? (Assume risk neutral drivers.) a) If the probability of detection with the extra police officer is 10%, then a speeding ticket should cost $55. b) If the probability of detection with the extra police officer is 10%, then a speeding ticket should cost $500. c) If the probability of detection with the extra police officer is 100%, then no one will speed. d) If the probability of detection with the extra police officer is 90%, then a speeding ticket should cost $59 e) None of the above