Answered: If X has a Pareto distribution with…

If X has a Pareto distribution with parameters α and β and if c is a positiveconstant, show that Y = cX has a Pareto distribution with parameters α and β/c.

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...

See similar textbooks

Related questions

Q: If x1, x2, . . . , xn are the values of a random sample from a normal population with the known…

A: Solution

Q: Suppose X, Y, Z are iid observations from a Poisson distribution with parameter λ, which is unknown.…

Q: Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from…

A: y^=-105+1.15xy¯=81.58x¯=168.11r=0.211P-value=0.035

Q: Consider a random sample X₁, X2,..., Xn from the following pdf (0x0-1 0≤x≤1 f(x) = {0x0. otherwise…

Q: Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from…

Q: Assume x follow to binominal with p=4/5 and p=1/5 and n=5 , Find maximum likelihood estimator.

A: X~Binomial (n,p)p(x)=nxpxqn-x Likelihood function L(p) = ∏i=1nnxp∑xiq∑n-∑xinL(p)=k p∑xiqn2-∑xi…

Q: Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from…

Q: Use the Distributions tool to find the t values that form the boundaries of the critical region for…

A: Critical value: Degrees of freedom = 21. From the EXCEL, using the formula, =T.INV.2T (0.05, 21),…

Q: Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and 189 cm and…

A: Answer The regression equation:Y^= -101 + 1.13x

Q: A class with 5 students has 3 juniors and 2 seniors. A group of 3 students is selected at random.…

A: Solution

Q: Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from…

A: Y^=-103+1.19X Given X=145

Q: A hypothesis test is to be performed for a population mean with null hypothesis of H0: u=u0 . The…

A: The given test is two-tailed and the significance level is 0.02.

Q: Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from…

A: Given data: The given regression equation is; y-cap = -103 + 1.04 x To find: The best predicted…

Q: Find the minimum mean square error forecast A forecast error e, (1) and Varfe, (1)1 for the…

Q: Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from…

A: The regression equation is

Q: Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from…

A: Note that P-value = 0.013 < 0.05 = alpha. Thus there is a linear relation between x and y.

Q: Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from…

A: To find : The best predicted value of y for an adult male who is 161cm tall .

Q: A shop receives a shipment of 1000 cheaply made lamps. The probability that any individual lamp is…

A: Let X be the number of defective lamps in the batch of 1000 which follows binomial distribution with…

Q: A hypothesis test is to be performed for a population mean with null hypothesis H: u=. The test…

A: Given data: Significance level = 0.01 Two tailed test We use Z-distribution

Q: Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from…

A: State the hypotheses. Null hypothesis: H0: Regression equation is not significant. Alternative…

Q: If you have a set of samples S= 0, 0, 1, 0, 1, 0 from a binomial distribution where P(x=0) = 1-μ and…

A: Given: A sample S=0, 0, 1, 0, 1, 0 is from a Binomial distribution where Px=0=1-μ and Px=1=μ.

Q: The lifetime X (in hundreds of hours) of a certain type of battery has a Weibull Distribution with…

Q: EXERCISE 3 Let X1, ..., X, be independent exponential random variables with mean 1/ß. Find the…

Q: Given W = (aX + Y)2 where X and Y %3D are zero-mean random variables with variance o2X =2, and…

A: Consider the provided question, W=aX+Y2 where X and Y are zero-mean random variables with variance…

Q: Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from…

Q: Suppose random variable X has a Poisson distribution with t = 2 and λ= 4. What is E(X)?

Q: Using the z-table, find the critical value with α = 0.10 for a left-tailed test.

Q: Consider a simple linear model (i.e., y is the dependent variable and z, is the covariate with…

A: Solution: From the given information, a simple linear model is The variance of the error term is

Q: Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from…

Q: sample x1=2, x2=3, x4=5 from iid Uniform(1,b). Find the maximum likelihood estimation of b

A: Given sample X1 = 2, X2 = 3, X4 = 5 Xi follows iid uniform(1,b)

Q: Let X1, X2, . . . , Xn be a random sample of size n from the exponential distribution with rate λ.…

A: Exponential Distribution: Understand the properties of the exponential distribution, including its…

Q: 1) Assume that a random variable Y has Weibull distribution with parameters a=2 and B=5. a) Find…

A: Given information: A random variable Y follows a Weibull distribution with parameters: It is…

Q: The joint cdf of a random variable X and Y is given by Fxy(x, y) = -e¯ª)(l-e-by) _x≥0, y ≥0, a, b>0…

Q: Let X1, . . ., Xn be a random sample from a gamma distribution with parameters α and β. Estimate the…

A: Given that be a random sample from a gamma distribution with parameters and .

Q: Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from…

A: Solution: Let X be the height of an adult male. From the given information, the regression equation…

Q: The AR model is a representative stable time series model and the random walk model is a…

A: Autoregressive model is a representation of a type of random process as such it is used to describe…

Q: Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from…

A: The question is about regression and correlation.Given :Randomly selected no. of adult males ( n ) =…

Q: Suppose that random variable X is uniformly distributed over the interval (0,1). Assume that the…

A: X follows U(0,1) Y|X follows B(n, x) E(X) = ½ E(Y|X) =nx

Q: Let X1, ..., X, be a random sample from a gamma distri- bution with parameters a and ß. a. Derive…

A: Given: Let X1,....Xn be a random sample from a gamma distribution with parametersα and β

Q: general form

A: Maximum Likelihood Estimation So far, we have discussed estimating the mean and variance of a…

Q: Suppose the variance of a regression model's stochastic error term is given by: Var(e) = o = 2.5, i=…

A: Given that The variance of a regression model stochastic error is given We have choose the correct…

Q: If the coefficient B, has a nonzero value, then it is helpful in predicting the value of the…

A: The null and alternative hypothesis is H0:β1=0H1:β1≠0

Q: If X is a uniformly distributed random varibale with a=8 and b=13, then Calculate the mean…

A: Answer: From the given data, X follows uniform distribution, a = 8 and b = 13

Q: Let X follow a uniform distribution with interval (0, 100] and Y be the excess loss random variable…

A: From the given information, X follows a uniform distribution with interval (0, 100]. Let YP be the…

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

If X has a Pareto distribution with parameters α and β and if c is a positive
constant, show that Y = cX has a Pareto distribution with parameters α and β/c.

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

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

Similar questions

Suppose a random variable X has a Bernoulli distribution for which the parameter O is unknown (0
This column contains data x1, . . . , xn, which is assumed to be a sample from a normal distribution N(µ, σ 2 ). For this sample, find the maximum likelihood estimates µˆ and σˆ.
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 139 to 194 cm and weights of 39 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x= 167.63 cm, y = 81.47 kg, r=0.106, P-value = 0.294, and y = - 108 + 1.04x. Find the best predicted value of y (weight) given an adult male who is 172 cm tall. Use a 0.05 significance level. The best predicted value of y for an adult male who is 172 cm tall is kg. (Round to two decimal places as needed.)
Without using a moment generating function; Prove that the variance of a beta-distributed random variable with parameters α and β is σ2 = αβ/[(α + β)^2 (α + β + 1)]
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 133 to 188 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.54 cm, y = 81.35 kg, r=0.186, P-value = 0.064, and y = - 109 + 1.12x. Find the best predicted value of ŷ (weight) given an adult male who is 180 cm tall. Use a 0.10 significance level. The best predicted value of y for an adult male who is 180 cm tall is (Round to two decimal places as needed.) kg.
There are 3000 stocks in the long-short stock market, which will be traded for 250 days in the next year. Set X and Y to be the daily holding amount of each stock And the return of the next day, and X and Y are respectively sampled from the normal distribution of N (0.100000NO, 2E-2). Use enough data to estimate Calculate the R2 of X and Y linear regression to be 001. Assume that positions among stocks are not correlated, and returns between stocks are not correlated. Define a day’s PNL as the day’s receipt beneficial PNL= 3000∑xy Find the expectation of PN and the sharpe rate of PNL every day
Let X1, X2, ..., X, be a random sample from f(x;0) = 0e-tI(0,00)(x). Find a 100y or (1- a)100 percent confidence interval for the mean of the population.
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 138 to 188 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.61 cm, y = 81.52 kg, r=0.271, P-value=0.006, and y = -103 +1.18x. Find the best predicted value of ŷ (weight) given an adult male who is 155 cm tall. Use a 0.10 significance level. The best predicted value of y for an adult male who is 155 cm tall is (Round to two decimal places as needed.) kg.
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 132 to 193 cm and weights of 39 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.59 cm, y = 81.52 kg, r= 0.416, P-value = 0.000, and y = - 102 + 1.13x. Find the best predicted value of y (weight) given an adult male who is 147 cm tall. Use a 0.05 significance level. The best predicted value of y for an adult male who is 147 cm tall is kg. (Round to two decimal places as needed.)
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 137 to 189 cm and weights of 37 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.50 cm, y =81.41 kg, r=0.232, P-value = 0.020, and y = - 109 + 1.17x. Find the best predicted value of y (weight) given an adult male who is 145 cm tall. Use a 0.01 significance level. The best predicted value of y for an adult male who is 145 cm tall is kg. (Round to two decimal places as needed.)
Let X1, X2, X3, ..., X, be a random sample from a distribution with known variance Var(X,) = o², and unknown mean EX, = 0. Find a (1 – a) confidence interval for 0. Assume that n is large.
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 137 to 192 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.80 cm, y = 81.45 kg, r=0.211, P-value = 0.035, and y = -103 +1.07x. Find the best predicted value of ŷ (weight) given an adult male who is 145 cm tall. Use a 0.01 significance level. The best predicted value of y for an adult male who is 145 cm tall is (Round to two decimal places as needed.) kg.