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- (3) Let X = b >(8,-) find E(5+6x) and distribution function.Suppose that the random change in value of a financial asset is X over the first day and Y over the second. Suppose also that Var(X) =18 and Var(Y) = 26 In this case, the total change in the value over these two days is given by X +Y. Do you have enough information to compute Var(X +Y)? If so, compute this value. If not, explain what additional information you need to do so.A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X = the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is as follows. The pdf is f(x) = kx^2 if 0 <= x <= 2, and 0 otherwise. (a) What is the probability that the lecture continues beyond the hour for between 30 and 45 sec? (Round your answer to four decimal places.)
- (13) Let X b(6,-) find E(5+6x) and distribution function. 3Varza) (16) Let X =U(3) find x) and distribution function.Calculate the mean and variance when the probability variable X's moment-generating function is as follows f(x)= 2x-1/16 , x=1,2,3,4 my answer is mean = 25/8, var = 170/16 - (50/16)^2 but solution is mean = 2, var = 4/5 How do we solve the problem? Help me
- 3. The length of time required by students to complete a 1 hour exam is a random variable with a pdf given by: f (x) = = ca + for 0 sæ<1 a. Find c. Enter c as a reduced fraction. C = b. Find F(x). Enter coefficients as reduced fractions and use ^ to denote powers. F(x) = c. Find the probability that a student takes less than 30 minutes to complete the exam. Enter the probability as a reduced fraction. prob = d. Find the median length of time to take the exam. Enter your answer in hours with 4 decimal places. median = hours e. Find the length of time for the first 10% of the students to complete the exam. Enter your answer in hours with 4 decimal places. hours answer = f. Find the expected value, variance, and standard deviation of X. Enter your answer in hours with 4 decimal places (or hours squared in the case of variance), hours expected value =Differentiate. f(w) = w / [w + (d/w)](16) Let X U(3) find Var(-x) and distribution function.
- Under the proportional reinsurance scheme of a certain risk S, the risk assumed by the insurer is S^A = aS, and the premium received is ap. Suppose that the initial capital of the insurer to cover said risk is u. Show that the default probability P (aS>ap + u) is an increasing function of a ∈ (0, 1).Q2. Prove that P(A^') = 1 − P(A), for any event ASuppose f"(x) = N(h) + a,h² + azh* + agh6 +.. The value of N,(h) using Richardson's extrapolation is: O N2 (h)=(4N1(h/2)-N1 (h))/3 with error of order O(h^2) N2 (h)=2N1 (h/2)-N1 (h) with error of order 0(h^2) N2 (h)=(4N1(h/2)-N1 (h))/3 with error of order O(h^4 ) N2 (h)=2N1 (h/2)-N1 (h) with error of order O(h)