We have three independent risks, each having the following probability mass functions:P(X₁=0)=1/4P(X₁=1)=1/2P(X₁=2)=1/4P(X₂=0)=1/2 P(X3=0)=1/4P(X₂=2)=1/2P(X3=2)=1/2P(X3=4)=1/4Determine the Value at Risk (VaR) (90%) and the Tail Value at Risk (TVaR) (90%) of the distribution of thetotal claims of the portfolio of 3 risks.

To calculate the VaR(90%) and TVaR(90%) of the distribution of the total claims of the portfolio of…

Answered: We have three independent risks, each…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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1) Suppose that Y₁, Y2,...,Y₁ is a random sample from a population with probability density function 1,7, f(x)=B³ Find the Maximum Likelihood Estimator of B. 00 elsewhere
A bank operates both a drive-up facility and a walk-up window. On a randomly selected day, let X be the proportion of time that the drive-up facility is in use (at least one customer is being served or waiting to be served) and Y be the proportion of time that the walk-up window is in use. The joint PDF is ... fxy (x, y) = 5 (x + y²) • What is the probability that neither window is busy more than one-quarter of the time? • What is f(X)? • What is fy(y)?
Establish the following: 0P (E)1 , P (A u B) = P (A) + P (B) – P (A n B) , P (A) = 1 – P (A’) ii The probability that a boy with a catapult hits target A is 2/3and that he hits target B is ¾. Given the probability of hitting both targets to be 1/2, find the probability that he (a) hits at least one of the targets (b) does not hit any. iii What is the probability of having at least one 6 in three throws with a dice?
The diameter of a round rock in a bucket, can be messured in mm and considered a random variable X in f(x) f(x) = k(x-x4) if 0 ≤ x ≤ 1f(x) = 0 otherwise. Find the expectation E(4X+ 3) and variance V(4X+3)
If the odds against T occurring are 8:5, then find P(T) and P(T'). P(T) = (Simplify your answer.) P(T') = (Simplify your answer.)
Find the mean and variance of X given the following probability density function:
You are given the following information regarding random variable X: I. E[X] = 2 II. E[X³] = 10 III. Var[X] = 1 Find E[(X – 1) ³].
1. Verify whether the following functions can be considered as probability mass functions: (i) P(x = x) = x² + 1 18 (iii) P(X= x) = -, x = 0, 1, 2, 3 (ii) P(X - x) - ²-2, -, x= 1, 2, 3 2x + 1 18 -, x = 0, 1, 2, 3 [Ans.: Yes) [Ans.: No] [Ans.: No]
2. Find E(X) and Var(X) if a. P(X = 0) = 0.2, P(X = 1) = 0.3, and P(X = 2) = 0.5. b. X is the number of successes in 200 Bernoulli trials each with probability of success 0.7.

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