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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.(13) Let X b(6,-) find E(5+6x) and distribution function. 3
- 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.)Varza) (16) Let X =U(3) find x) and distribution function.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 =
- 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 meshow that 1-2% show that B(wn) p(ntt, n+t) =표산에.(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)