1. The policy holder's loss function, X follows a distribution,,X = 2P(x) = {,x =4.,X = 6Find (i) the moment generating function(i) Mean of X using the moment generating functionN|00m 100 l00

Distribution of X is given as X 2 4 6 P(x) 28 38 38 i) Moment Generating function :…

Answered: 1. The policy holder's loss function, X…

1. The policy holder's loss function, X follows a distribution, ,X = 2 8. P(x) = {=,x =4 . 3 x = 6 Find (1) the moment generating function (ii) Mean of X using the moment generating function

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: 1. Consider the following time series: a. Construct a time series plot. What type of pattern exists…

Q: IEX is a Poisson distribution variable, then its moment generating function is e^(e' -1).

Q: 1. Suppose observations yt follow a linear trend + white noise stochastic process: yt = c + βt + ϵt…

A: Given yt = c + βt + εt, where εt ~ WN0, σ2

Q: The U.S. divorce rate has been reported as 3.6 divorces per 1000 population. Assuming that this rate…

A: Hi, thanks for posting the question. Since there are more than three sub parts posted in the…

Q: Suppose X has an exponential distribution with parameter A=1 and Y|X = z has a Poisson distribution…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…

Q: 3.2 Explain how you would find the moment-generating function for an exponential-distributed random…

A: As per bartleby guidelines we can solve only one question and rest can be reposted

Q: Suppose X has a Poisson distribution with parameter A and suppose the conditional distribution of Y…

Q: Example 17.18. Obtain the MVB estimator for u in normal population N(µ, ở), where o? is known.

Q: Your friend, Lajos, wanted you to settle his hunch that the daily average of the number of customers…

Q: What is the relationship between B1, ôxy, and ô? Express this relationship mathematically. Could ôXY…

A: Let Y=β0^+β1^X be an estimated simple linear regression. Then, the covariance of X and Y will give…

Q: For each of the following scenarios, identify: the population of interest, the outcome variable…

A: Given: Two scenarios

Q: Consider the random walk from HW3 Task 1 with a boundary of [-3, 3] depicted below. What is the…

A: The provided graph is:

Q: 7. a) Suppose we have the following data for a Cobb-Douglas production function, including its…

A: Given: Year Real gross product (millions of NT $)°, Y Labor days (millions of days) X2 Real…

Q: Let X1, X2, .., X10 be a random sample from a gamma distribution with a = 3 and ß = 1/0. Suppose we…

Q: x 1 2 3 4 5 P(X=x) 0.21 0.197 0.2 0.173 0.22 use the information in Table 3 to determine the…

A: Considering the score of 5 to be the score that exceeds the required standard for practices towards…

Q: Suppose a quality control expert examines iterms for defects in a series of independent fixates,…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Suppose the reaction temperature X (in °C) in a certain chemical process has a uniform distribution…

Q: Some previous studies have shown a relationship between emergency-room admissions per day and level…

Q: The table below indicates an urban zone's expected houschold composition at some future year and the…

A: Given,A table that shows an urban zone's expected household composition.To find: Total…

Q: 5. Suppose that X1, X2, .. ,X, are an iid sample from the distribution given below, f(X)e = (1/2)(1+…

Q: 1. For each of the following scaling functions for a von Neumann-Morgenstern utility func- tion,…

Q: Example 4.15 Let (X1, X2. .... X,) be a random sample from the exponential dis- tribution with PDF…

Q: Question is attached.

A: Given thatThe moment generating function of a random variable isTo find mean and variance:

Q: Let ~ U(0, 1). Show that X =-2ln(Y) follows an Exponential distribution with mean 2.

A: Given that Y follows Uniform(0,1) And X = -2ln(Y)

Q: The U.S. divorce rate has been reported as 3.6 divorces per 1000 population. Assuming that this rate…

A: Hey there! Thanks for posting the question. Since there are more than three sub-parts in your…

Q: B. Which of the following will NOT affect a firm's beta? 1) the choice of the market portfolio…

A: (2).the choice of the risk free security

Q: 9. If the moment generating function of X is 2 2 e' + M find the mean, variance and p.d.f. of X.

Q: 1. The means and standard deviations of absenteeism index from samples of 100 nightshift students…

A: (a) The null and alternative hypothesis is, The type of test is right tailed test (b) The value of…

Q: 3. If X has a Poisson distribution and if P(X = 0)3D0.25, find P(X > 4).

A: Here, P(X=0) =0.25 That is, PX=0=0.25 e-λλ00!=0.25 e-λ=0.25 λ=-In0.25…

Q: 3- The variance of the random variable is the second derivative of the moment generating function…

A: The moment-generating function of a random variable X is: {\displaystyle M_{X}(t):=\operatorname…

Q: 1, Assume you are managing a manufacturing line consisting of two workstations: Decambering and…

A: Assume you are managing a manufacturing line consisting of workstations: Decambaring and Hemming.…

Q: Suppose the reaction temperature X (in °C) in a certain chemical process has a uniform distribution…

A: Let X denote the reaction temperature. Given that X follows Uniform(A = -6, B = 6). Then the…

Q: 5. Suppose that X1, X2, ... , Xn are an iid sample from the distribution given below, f(X)e =…

A: Let X1,X2,...,Xn be a random sample of size n with probability density function(pdf) f(x) then the…

Q: Find a value for the product moment correlation coefficient r for this data Explain what the…

A: here given, formulae: product moment correlation coefficient r=SxySxxSyy Sxy=∑(xi-x )(yi-y )…

Q: 19! Suppose X has a Poisson distribution with parameter uniformly most powerful test of Ho : A 1…

A: Question of the problem : Find the UMP level α test for Ho : λ = 1 vs. H1 : λ > 1. First , Find…

Q: Suppose the reaction temperature X (in °C) in a certain chemical process has a uniform distribution…

A: We have given that, Let X be random variable are uniformly distributed with A= -6 and B= 6 Then,…

Q: 27. The normal approximation to the Poisson distribution X with mean is X ~ N() X ~ N(4) c N(4) D X~…

A: for Poisson distribution X mean λ=14

Q: 2. Suppose that in a certain chemical process the reaction time y (hour) is related to the…

A: We have to answer questions based on simple linear regression method.

Q: Suppose the reaction temperature X (in °C) in a certain chemical process has a uniform distribution…

Q: 8. Suppose people enter a waiting room according to a Poisson process of rate A. Whenever there is a…

A: we have given that, X = entering in a waiting room follows poisson with parameter λ therefore, pdf…

Q: Example 24: If a random variable X has the moment generating function Mx (t) = 2-t' 2 determine the…

Q: 3. Suppose Barney has a vNM utility u(0) = 0, u(10) = 0.7 and u(20) = 1. What is the slope of his…

Q: The US divorce rate has been reported as 3.6 divorces per 1000 population. Assuming that this rate…

A: Hey there! Thanks for posting the question. Since there are more than three sub-parts in your…

Q: 13. If X has the distribution function for x<-1 1 for -1 sx< 1 Fx) for 1sx<3 for 3sx<5 for xz5 find…

Q: In a given time series: Y1, Y2, Y3, ..., we expect there is: **** OA. autocorrelation in the Y's. B.…

A: State which of the following is true:

Q: Suppose you simulate the price path of stock HHF using a geometric Brownian motion model with µ =…

A: From the given information, μ=0.1 σ=0.2 ∆t=1/52 S0=100 ε=-0.591

Q: dollars. In addition, suppose that after the value has been observed , the 2022 team budget, say ,…

A: Given, Suppose that you enter a fantasy baseball league. Suppose that the 2021 team budget, say , is…

Q: 2. Find a data set of economic/financial time series with one y variable and two independent…

A: Data set: Year GDP Education spend Unemployment rate 2000 256376 14185 7 2001 264335…

Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

1. The policy holder's loss function, X follows a distribution,
,X = 2
P(x) = {,x =4.
,X = 6
Find (i) the moment generating function
(i) Mean of X using the moment generating function
N|00m 100 l00

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Correlation, Regression, and Association$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

The lifetime of a certain type of TV remote control is given by Y . Suppose Y has approximately exponential distribution with mean 8 years. a) Find the probability that a remote control of this type will last more than 15 years. b) Find the probability that of eight such remote controls at least one will last more than 15 years. c) What should the warranty period for these remote controls be if the manufacturer wants 85% of the remote controls to last beyond the warranty period? d) What is the moment generating function of Y .
1.9.5. Let a random variable $X$ of the continuous type have a pdf $f(x)$ whose graph is symmetric with respect to $x=c .$ If the mean value of $X$ exists, show that $E(X)=c$Hint: Show that $E(X-c)$ equals zero by writing $E(X-c)$ as the sum of two integrals: one from $-\infty$ to $c$ and the other from $c$ to $\infty .$ In the first, let $y=c-x$ and, in the second, $z=x-c .$ Finally, use the symmetry condition $f(c-y)=f(c+y)$ in the first.
Derive a general expression for the variance of net future loss Var(L) with a constant force of interest δ under each of the following models:i. μ_x(t) = μii. μ_x(t) = 1/(ω-x)
2) The time between successive customers coming to the market is assumed to have Exponential distribution with parameter l. a) If X1, X2, . . . , Xn are the times, in minutes, between successive customers selected randomly, estimate the parameter of the distribution. b) b) The randomly selected 12 times between successive customers are found as 1.8, 1.2, 0.8, 1.4, 1.2, 0.9, 0.6, 1.2, 1.2, 0.8, 1.5, and 0.6 mins. Estimate the mean time between successive customers, and write down the distribution function. c) In order to estimate the distribution parameter with 0.3 error and 4% risk, find the minimum sample size.
Suppose a quality control expert examines iterms for defects in a series of independent fixates, each of a fixed duration, and suppose that defects are present. Let p be the probability that the defect or flaw is detected and 1-p the probability that a defect or flaw is not detected. Let the r.v. X = the number of defects detected in n fixations. a. What is the pmf of X? b. What is the expected value of X = E(X)? c. What is the moment generating function (mgf) for the r.v. X (Remember to state the interval of validity for t)? d. Use it to find the Variance of X.
Consider two securities, the first having μ1 = 1 and σ1 = 0.1, and the secondhaving μ2 = 0.8 and σ2 = 0.12. Suppose that they are negatively correlated,with ρ = −0.8. Denote the expected return and its standard deviation as functions of π byμ(π ) and σ (π ). The pair (μ(π ), σ (π )) trace out a curve in the plane as πvaries from 0 to 1. Plot this curve in R.
Suppose that you enter a fantasy baseball league. Suppose that the 2021 team budget, say , is randomly drawn from a uniform distribution on the interval , where the unit is U.S. million dollars. In addition, suppose that after the value has been observed , the 2022 team budget, say , is randomly drawn from a uniform distribution on the interval . In other words, the 2022 budget is at most as large as the 2021 budget. a) For any given value of x(50<x<350), obtain E[Y|X=x] b) In view of part (a), obtain E[Y|X] c) Atlanta Braves won the 2021 World Series title. Their estimated 2022 payroll is about $130 million. Would your 2022 fantasy baseball budget be on average larger than their 2022 payroll? Explain briefly.
Consider a stable single-station queue. Suppose it costs $c to hold a customer in the system for one unit of time. Show that the long-run holding cost rate is given by cL, where L is the mean number of customers in steady state.
Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample? I asked this question earlier today, but didn't quite understand all of the response. P(y1<=yn)p(y2<=yn) and so on was used, but shouldn't the yn be listed first in the inequality since we want to know if yn is the smallest?
LetX1,X2,...,Xn be a sequence of independent and identically distributed random variables having the Exponential(λ) distribution,λ >0, fXi(x) ={λe−λx, x >0 0, otherwise Define the random variable Y=X1+X2+···+Xn. Find E(Y),Var(Y)and the moment generating function ofY.
1i. Suppose that a structure can withstand a flood with a peak discharge no greater than 1,950 m3/s and it has been designed to have an economic life span of 100 years. Determine the risk of failure assuming the Extreme Value Distribution when the mean and standard deviation of the annual flood series are 410m3/s and 280 m3/s, respectively. 1ii. What is the probability that at least one flood of ARI 50y (T=50y) will occur during the 30 year design life of a flood control project? 1iii. Consider a small, temporary (3 year design life) flood mitigation dam designed to contain a 20 year flood event. What is the risk that it will be overtopped at least once in the design life.
Suppose that X is a continuous unknown all of whose values are between -5 and 5 and whose PDF, denoted f, is given by f ( x ) = c ( 25 − x^2 ) , − 5 ≤ x ≤ 5 , and where c is a positive normalizing constant. What is the expected value of X^2?