3. Suppose that Y is a random variable with moment generating function My (t). Suppose further that X is a random variable with moment generating function Mx(t) given by 1 Mx(t) = (2e³t + 1) My(t). Given that the mean of Y is 0 and the variance of Y is 1 then determine the mean and variance of X.
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- If the estimator is consistent and the asymptotic variance is smaller than all other consistent estimators of then Ô is asymptotic efficient. O True FalseThe mean of X = 10 and the standard deviation of X = 2. The variable X is linearly transformed such that Xnew = a + bX. The mean of Xnew = 800 and the variance of Xnew = 100. Suppose b is a negative number. What does a equal? 4. The mean of X = 5 and the variance of X = 4. The variable X is linearly transformed such that Xnew = a + bX. The mean of Xnew = 400 and the standard deviation of Xnew = 6. Suppose b is a negative number. What does a equal? 5.4. There are 10 keys and only one of them can open a lock. We do not know which key can open the lock, but we will try them one by one until we find the right key. Let X denote the number of times tried to find the right key. (a) What is the p.m.f. of X? (b) What is the C.D.F. of X? (c) What is the mean and variance of X?
- Suppose the market for auto insurance is made of up two types of buyers: high-risk and low-risk. Buyers’ willingness to pay (WTP) for auto insurance plans, and sellers’ willingness to accept (WTA) when selling plans to each type of buyer, are outlined in a photo Assume now that there is asymmetric information and that insurance companies do not knowhow risky an individual buyer is. In the face of this uncertainty, they determine that the probability that a “walk-in” is high-risk is 0.75. What is the minimum price sellers are willing to accept when selling aninsurance plan? At this price, will low- and high-risk buyers both be willing to purchase this insurance plan? Explain. Be sure the mention adverse selection in your answer. Returning to the conditions outlined in Q1, suppose that buyers of auto insurance (high- and low-risk) were offered a $1,000 subsidy to purchase coverage. This would raise their WTP by $1,000. Would the market for both insurance plans clear after the…No written by hand solution3. Consider again the information above. Suppose that in reality our usual assumptions on the e terms hold (they have constant variance, and are uncorrelated). Suppose you have a friend who insists the appropriate estimator of B, is: À = E) - A Derive the variance of this estimator of B1.
- Strictly Note ->( Provide solution for the last two parts [d and e]) Don't use ai and answer properly with proper solution and explanantion of for steps. please help me out AsapSuppose there are n assets which are uncorrelated. (They mightbe n different “wild cat” oil well prospects.) You may invest in any one, or in any combination of them. The mean rate of return r¯ is the same for each asset, but the variances are different. The return on asset i has a variance of σ2i for i = 1, 2, . . . , n.(a) Show the situation on an r¯-σ diagram. Describe the efficient set.(b) Find the minimum-variance point. Express your result in terms of σ¯2 =!"ni=11σ2i#−1.18. An insurance agent has claimed that the average age of policy-holders who insure through him is less than the average for all agents, which is 30-5 years. A random sample of 100 policy-holders who had insured through him gave the following age distribution : Age last birthday 16-20 21-25 26-30 31-35 36-40 No. of persons 12 22 20 30 16 : Calculate the arithmetic mean and standard deviation of this distribution and use these values to test his claim at the 5% level of significance. You are given that Z (1-645) = (0-95.
- Show me full answers and steps to part d) and e) Don’t use R or excel formula. Use expected formula and mean formula to calculateSuppose that the distribution of Uber rides around the quoted arrival time is normally distributed. Themean waiting time (relative to the quoted time) is 0, with a standard deviation of 3 minutes.a. Using the empirical rule, what percentage of rides arrive within 3 minutes of the mean (3 minutesbefore to 3 minutes after)?b. Graphically depict the area that would need to be calculated to determine the probability ofwaiting more than 4 minutes for a ride. Explain your graph.A store sells from 0 to 12 computers per day. Is the amount of daily computer sales a discrete or continuous random variable?