If X is a random variable whose pdf belongs to the k-parameter exponential family, thenac:@ d;(X)In a(0)Ei=1kaci@ d;(X)In a(@)Var )- E-d;(X)> TASK # 28:Determine whether f (x) = 1²xe-1xI(0,00) is a valid pdf or not.If it is valid, can you use the theorem above to derive the variance ofX~F? If Yes, find the mean and variance of X using the theoremabove.If f is not valid, correct it to becomes a valid pdf then proceed to thepart of finding its mean and its variance.

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Answered: If X is a random variable whose pdf…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose that we want to build a model that predicts the group membership of a hurricane, either tropical (0) or non-tropical (1) based on the latitude of formation of the huricane. The response variable is the binary variable Type.new (type of hurricane) and the predictor variable is FirstLat (First Latitude). Using R, we build a model by applying the glm () function. For the logistic regression model, we specify family = "binomial". The data is available at https://userpage.fu-berlin.de/soga/200/2010 data sets hurricanes.xlsx. The R code is #set up filename my.filename 1z|) <2e-16 *** 0.96148 -9.446 0.37283 0.03947 9.447 <2e-16 *** --- *# Signif. codes: 0 '*** 0.001 **' 0.01 '*' 0.05'.' 0.1 '' 1 # (Dispersion parameter for binomial family taken to be 1) Null deviance: 463.11 on 336 degrees of freedom *# Residual deviance: 232.03 on 335 degrees of freedom *# AIC: 236.03 *# Number of Fisher Scoring iterations: 6 What is the interpretation of the p-value of the predictor variable…
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Consider that a pdf of a random variable X is 1 -25x53 fx (x) ={K otherwise and another random variable Y = 2X. Then find (a) value K, (b) E[X], (c) E[Y] and ( d) EΧΥ.
Suppose you obtain the following regression model, E[y]=91+79*x1 +20*x1*x2. What is the impact of a 39 unit change of x1 on the expected value of y when x2 is at its mean of 40?
f(X)= 3/8( 4x - 2x2 ) 0<* x <* 2 (* less or equal to) a. Find the variance of X.
Consider the logit regression log(odds(QualExam) = ßo + B, • ParEduc + B, • Awards. where QualExam is a binary variable that indicates passing the exam if equal to 1, and failing the exam if 0, ParEduc indicates the parents' education level, and Awards is a binary variable that indicates having experience of obtaining award(s) if equal to 1, and not having experience if 0. Given the parents' average education level unchanged, the odds ratio is expected to be _ for an individual with awards to pass the exam comparing to those without awards. For an individual without awards and the parents' education level of 4, the estimated probability of passing the exam is approximately_. ParEduc Awards Intercept -10.53 2.98 0.48 O A. 0.48; 80%. O B. 1.616; 80%. O C. 1.616; 4%. O D. 0.48; 4%.
Suppose the random variable T is the length of life of an object (possibly the lifetime of an electrical component or of a subject given a particular treatment). The hazard function hr(t) associated with the random variable T is defined by hr(t) = lims-o- P(t ≤ T
Derive the following:(c) variance(d) moment generating function
Suppose that each individual in a large insurance portfolio incurs losses according to an exponential distribution with mean 1/2,where i varies over the portfolio according to a G(a, 3) mixing distribution. The respective densities of the two distributions are given by Sx (x) = (1/2) exp (-x/à), x > 0, 2 > 0; S(2) =- T(a) 2-l exp(-8i), 2 > 0. Given that the Pareto pdf given by fx (x) = (5 +x)ª+1 * > 0, a > 0, 8> 0. (a) Show that the marginal distribution of losses follows a Pareto distribution, i.e. P(a, 5). (b) Use the mixing formulation of the Pareto to deduce that if X~P(a, 5), then E (X) = .

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