What is the variance of u conditional on income, vartul inc)? Consider the following savings model: Where inc income and sav = savings A. var(inc*e) OB. inc*var(e) OC var(sqrt(inc)) OD. var(e) sav = Bo + Brinc + u, u = Vince
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- Consider the lottery that assigns a probability T of obtaining a level of consumption CH and a probability 1-T of obtaining a low level of consumption c, with CH > C1. Consider an individual facing such a lottery with utility function u(c) that has the properties that more is better (that is, a strictly positive marginal utility of consumption at all levels of c) and diminishing marginal utility of consumption, u"(c) < 0. As usual, we are using the shorthand u'(c) consumption and u"(c) = " = dư ( to be the second derivative of the utility function (which is also the derivative of the first derivative of the utility function). du(c) for the first derivative of the utility function with respect to dc du(c) dc2 du' (c) dc1. The following table gives the PDF (Probability Density Function) of the discrete variable X X -1 -2 2 3 4 f(x) 0.1 0.2 0.1 0.3 0.1 0.2 Calculate the E(x) (expectation) and var(x) (variance) 2. Prove the following properties of expectation and variance: If a and b are constants, X and Y are random variables, then E(aX+b)=aE(x)+b var (aX+ b) = a² var (X) var (X+ Y)= var (X) + var (Y) +2 cov(X, Y) =var (X) + var (Y) + 2pox0y Of which p is correlation coefficient, oz and o, are standard error of X and Y. 3. Assume that X- N(6, 4). What is the probability that 2 10?The promoter of a football game is concerned that it will rain. She has the option of spending $14,040 on insurance that will pay $39,000 if it rains. She estimates that the revenue from the game will be $65,040 if it does not rain and $30,040 if it does rain. What must the chance of rain be if buying the policy has the same expected return as not buying it? Write expressions showing the expected returns if the promoter does and does not purchase the insurance, using p to represent the probability of rain. Without insurance, E(return) = With insurance, E(return) = The chance of rain must be _%.
- View image and please calculate for first funciton.Please no written by hand solution Kate recently invested in real estate with the intention of selling the property one year from today. She has modeled the returns on that investment based on three economic scenarios. She believes that if the economy stays healthy, then her investment will generate a 30 percent return. However, if the economy softens, as predicted, the return will be 10 percent, while the return will be -25 percent if the economy slips into a recession. If the probabilities of the healthy, soft, and recessionary states are 0.6, 0.2, and 0.2, respectively, then what are the expected return and the standard deviation of the return on Kate❝s investment? Calculate the coefficient of variation for this investment. (Round expected return to 3 decimal places, e.g. 0.125 and round intermediate calculations and standard deviation to 5 decimal places, e.g. 0.07680.)Compute the Posterior Probabilities by completing the table
- 21. The amount of bread (in hundreds of pounds) x that a certain bakery is able to sell in a day is found to be a numerical valued random phenomenon, with a probabiliiy function specified by the p.d.f. f(x), given by : k. x ={k. (10 – x), for 52please explain how to solve this; (answers of this question is provided) Asap please... I vll definitely upvoteSEE MORE QUESTIONS