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- If X1, X2, ... , Xk have the multinomial distribution of Definition 8, show that the mean of the marginal distribu-tion of Xi is nθi for i = 1, 2, ... , k.6. The amount of a loss X follows the uniform distribution on [0, 100]. An insurance policy on this loss has an ordinary deductible of 10, a maximum amount paid of 50, and a coinsurance of 80%, which is applied after the deductible. After losses are subject to inflation of 10%, calculate the expected claim amount paid per loss on this policy.6. Given a continuous uniform distribution, show that A+B (a) μ = and 2 (b) 02: (B-A)² = 12
- 2.Suppose that the return R (in dollars per share) of a stock has the uniform distribution on the interval [-3,7]. Suppose also, that each share of the stock costs $1.50. Let Y be the net return (total return minus cost) on an investment of 10 shares of the stocks. Compute E(Y).الموافق foo an exponentiaL distribution fx Cx jt) e.w. where u>o Write (Dankderive) meancespedoed V9lue) f.eECx)Let X1, X2,...X100 be the annual average temperature in Paris in the years 2001, 2002, ..., 2100, respectively. Assume that average annual temperatures are sampled i.id. from a continuous distribution.(Note: For this problem, we assume the temperature distribution doesn't change over time. With global warming, this is not a good assumption.)A year is a record high if its average temperature is greater than those in all previous years (starting with 2001), and a record low if its average temperature islower than those in all previous years. By definition, the year 2001 is both a record high and a record low.1. In the 20 century (the years 2001 through 2100, inclusive), find the expected number of years that are either a record high or a record low.2. Let N be an r.v. representing the number of years required to get a new record high after the year 2001. Find P(N > n) for all positive integers n, and use thisto find the PMF of N.3. Check answers to parts (1) and (2).4. Explain how…Let. X have a uniform distribution on the interval (1,3). What is the proba- bility that the sum of 2 independent observations of X is greater than 5?The ratio of selling prices of a security on consecutive days has a lognormal distribution with parameters u = 0.02 and o = 0.06. a. What is the probability of a one-day increase in the selling price? b. What is the probability of a five-day decrease in the selling price?Each statement below is incorrect. Justify why it is incorrect and give the correct distribution with its parameter(s) value if possible. a) Students arrival to school were Poisson -distributed with an average of 3 students per 1 minute. Therefore, the waiting time for the arrival of 3 students is exponentially distributed with 0= 1/3.Move to Archive x 0.3e If 1-.7et is the mgf of a well known function. It is Geometric mgf i) Its name is ii) The mean of this distribution = iii) P(x = 4) = iv) The variance of this distribution is2.) Use the moment generating function you just proved to verify that for a Poisson distribution, E(X) = λ and Var(X) = λ.In this question you are required to examine distribution at X(0) and x(1/8fo) x(0) ∈{0,-1 ,1} X(1/8fo)∈{1/(√2), -1/(√2)} Show that is not strict sense stationarySEE MORE QUESTIONS