Let X and Y be random losses with joint density function fx,y (r, y) = 2x for 0 < z <1 and 0 < y< 1. An insurance policy is written to cover the loss X+Y. The policy has a deductible of 1. Calculate the expected payment under the policy. Possible Answers 1/4 B 1/3 C 1/2 7/12
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- 7. Assume that X and Y have joint probability density function given by (2x + 3y) if 0< x<1 and 0Thank you.Ex. Let X be a Gamma distribution with parameter (a, 1). 1 -de-d* (2r)ª-1 for 0<=x<∞. T(a) f(x). Calculate My(1) :4. Find k such that the following are probability density functions: (a) f(x) = k(2x), 02. Assume X,~N (µ,o²). Let T=(1/n)E(x, -x)', T; = (1/(n – 1))E(x, -x)'. %3D 2 Find the expected value of each above function.The exponential distribution is a probability distribution for non-negative real numbers. It is often used to model waiting or survival times. The version that we will look at has a probability density function of the form p(y|v) = exp(-e¯ºy — v) (1) where y R+, i.e., y can take on the values of non-negative real numbers. In this form it has one parameter: a log-scale parameter v. If a random variable follows an exponential distribution with log-scale v we say that Y~ Exp(v). If Y~ Exp(v), then E [Y] =e" and V [Y] = e²v. 1. Produce a plot of the exponential probability density function (1) for the values y E (0, 10), for v = 1, v = 0.5 and v= 2. Ensure the graph is readable, the axis are labeled appropriately and a legend is included. ta il 2. Imagine we are given a sample of n observations y = (y₁,..., yn). Write down the joint proba- bility of this sample of data, under the assumption that it came from an exponential distribution with log-scale parameter v (i.e., write down the…Given: image Find the following: show sol. a) Conditional pdf of Y given X=x b) Conditional Expectation of Y given X=x c) Conditional variance of Y given X=xX and Y re random losses with joint density funcTion 2C forocn<00 500000 An Insurance losses pays the total of the twX9 losses to a maximum and oey< lo0, 100 policy on the payment of 100 the expectic fpagment the insurer will make on this policy.5. Determine the value of c that makes the function f (x, y) = c(x + y) a joint probability density function over the range 0 < x < 3 and 0 < y < x. Answer is C = 2/27 a. From the answer in Question 5, Determine the marginal probability distribution of X. b. From the answer in Question 5, Determine the conditional probability distribution of X given that Y = 2. c. From the answer in Question 5, Determine E(Y | X = 1). (up to 6 decimal place)Let X1, X2, X3, be a r. s. from normal distribution with mean 0 and variance 1, let the prior distribution of 0 is normal with mean zeroand variance 1. Let L(6,0) = (ô - 0). Find the Bayes estimator of 0Let X represent the lifetime of a component, in weeks. Let Y represent the lifetime of the component in days, so Y = 7X. Suppose X ~ Exp(1). Let Fy be the cumulative distribution function of Y and let Fy be the cumulative distribution function of X. Show that Fy(y) = 1 e¯e-Ày/7. [Hint: F,(y) = P(Y < y) = P(7XУк. Suppose that Y₁. Y₂; Yn 15. 2 from Function random Sample a population with probability density f(y) = find the maximum BY 1-B B like hood ozy 21: B >0 Elsewhere Estimator of BSEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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