here cumulative distribution function:G(y)= P(Y<y) =P(max(X1,X2)<y)
=P(X1<y)*P(X2<y)=(y/5)*(y/5) =y2/25
option B is correct
The circled answer is wrong Just show steps to arrive at a correct answer please. (19)...
The circled answer is wrong, please show steps to arrive at a correct answer. (17) Assume X and Y have the following joint density function: f(x,y) =-(x + y), 0<x<2,0<p<2 Calculate P(X +Ys 1). B) C) 17 24 A) E) 24 24
4a). Let X1 and X2 be independent random variables with a common cumulative distribution function (i.e., c.d.f.) F(y) = { 0" if0cyotherwise。 Find the p.d. f. of X(2,-max(X, , xa). Are X(1)/X(2) and X(2) independent, where X(1,-min(X,, X2) ? 4a). Let X1 and X2 be independent random variables with a common cumulative distribution function (i.e., c.d.f.) F(y) = { 0" if0cyotherwise。 Find the p.d. f. of X(2,-max(X, , xa). Are X(1)/X(2) and X(2) independent, where X(1,-min(X,, X2) ?
The circled answer is wrong, show steps to arrive at a correct answer please. 9) Assume that the number of hurricanes during a given year follows a Negative Binomial distribution where r-4 and p-31%. Investor A and Investor B have entered an agreement where Investor A will pay Investor B $1,000,000 in the event that a hurricane does not occur. Given the probability density function for a Negative Binomial is P(X = n) = (n+r-1 calculate the expected payment that...
The circled answer is wrong please show steps to arrive at a correct answer. Company ABg offers hurricane insurance to homeowners in Texas. Assume that the premium collected for hurricane insurance can be modeled by an Ex- ponential distribution with a mean of 3. Suppose that the hurricane losses can be modeled by an Exponential distribution with a mean of 1. If the premium collected and hurricane losses are independent, what is the probability that the ratio of losses to...
(7) Let X1,Xn are i.i.d. random variables, each with probability distribution F and prob- ability density function f. Define U=max{Xi , . . . , X,.), V=min(X1, ,X,). (a) Find the distribution function and the density function of U and of V (b) Show that the joint density function of U and V is fe,y(u, u)= n(n-1)/(u)/(v)[F(v)-F(u)]n-1, ifu < u. (7) Let X1,Xn are i.i.d. random variables, each with probability distribution F and prob- ability density function f. Define U=max{Xi...
The circled answer is wrong please show all work to arrive at a correct answer (23) Let X and Y represent the number of hours that a person spends cooking and doing the dishes, respectively, during a 30-day period. Assume that during a 30 -day period, the ex pected number of hours that a person spends in cooking is 20, with a variance of 40. Also assume that during a 30-day period, the expected number of hours that a person...
3.21. Problem. (Section 11.2) In each of the following cases below, assume that X and Y are independent random variables then use the Convolution Theorem to derive the proba- bility density function of X +Y. (a) The random variable X is uniform distribution on 0, 1) and the random variable Y is an exponential distribution with = 0.2. (b) The random variable X is a uniform distribution on (0, 2) and the random variable Y is a uniform distribution on...
Let Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter p. Suppose that Y, X1 and X2 are independent. Proof using the de finition of distribution function that the the distribution function of Z =Y Xit(1-Y)X2 is F = pF14(1-p)F2 Don't use generatinq moment functions, characteristic functions) Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter...
The circled answer is wrong please show the work to arrive at a correct answer please. n insurance policy reimburses 100% for losses up to $100, less a deductible. In addition, the policy reimburses 50% of losses beyond $100. The deductible is $20 and losses follow an Exponential distribution with mean $80. Calculate the probability that the reimbursement for a loss is less than $100, given that (12) the reimbursement is greater than SO A) 0.202 B) 0.632 (C)0.736 D)...
I don't understand a iii and b ii, What's the procedure of deriving the limit distribution? Thanks. 6. Extreme values are of central importance in risk management and the following two questions provide the fundamental tool used in the extreme value theory. (a) Let Xi,... , Xn be independent identically distributed (i. i. d.) exp (1) random variables and define max(Xi,..., Xn) (i) Find the cumulative distribution of Zn (ii) Calculate the cumulative distribution of Vn -Zn - Inn (iii)...