Exercise 3. Let X be a random variable with mean u and variance o2. For a E R, consider theexpectation E((X – a)²).a) Write E((X – a)²) in terms of a, µ and o2.b) For which value a is E((X – a)²) minimal?c) For the value a from part (b), what is E((X – a)²)?

Farmula used V(X)=E(X2)-[E(X)]2

Answered: Exercise 3. Let X be a random variable…

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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let x has the p.d.f {2.xe-v2x 0
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Exercise 3. Let X be a random variable with mean µ and variance o². For a € R, consider the expectation E((X − a)²). a) Write E((X - a)²) in terms of a, μ and σ². b) For which value a is E((X − a)²) minimal? c) For the value a from part (b), what is E((X − a)²)?
A firm's revenue R is stochastically related to the effort exerted by its employee. Effort is a continuous variable. The employee can choose any level of effort e E [0, ). The choice of effort affects revenue so that: E(R|e) = e and Var(R|e) = 1 %3D where E(R|e) and V ar(R|e) denote the expected value and variance, respectively, of rev- enue when the employee exerts effort level e. The employer cannot observe the level of effort exerted by the employee. The employer wants to design a wage contract w based on the revenue and considers only contracts of the form: w-α+ βR and so the employee is guaranteed a payment a and then a bonus payment ßR which de- pends on revenue. The employee is a risk-averse expected utility maximiser. A contract w gives expected utility: Eu(w\e) = E(w\e)-eV ar(w]e) – c(e) where E(wle) and Var(wle) denote the expected value and variance of the contract, re- spectively, conditional on effort e, p is a parameter of risk aversion, and c(e) denotes the disutility of…
Suppose that Y is an exponential random variable with λ = 4. Find. P[Y > (E(Y) + 2√√Var(Y))] . (round to 4 decimal points)
The variance of Y is σ2y = 4.6875 and the variance of the sum is σ2x + y = 9.1875. You knowthe variance of X=1. Find the covariance, xy. Show work
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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
1. Let X be an RV with PDF a. Find the mean of X. b. Find the variance of X. f(x) = {¹ -=| - |x| for x < 1 otherwise
*2. Let log Y the median of Y). ~ N (u, o2). Find the distribution of Y and show that P(Y < eH) = 0.5 (i.e., el is
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1. The incidence of cancer among phosphate mine workers and their exposure to radiation was investigated. Cancer incidence was recorded among 60 phosphate mine workers who had 0-29 working level months (WLM) of exposure, 60 phosphate mine workers who had 30-89 WLM of exposure, and 60 phosphate mine workers who had 90-120 WLM of exposure. The number of cancer incidences for each group are presented in Table 1. Table 1: Two-way Table of Counts Cancer Incidence Exposure Level Yes No Total 0-29 WLM 20 40 60 30-89 WLM 33 27 60 90-120 WLM 43 17 60 Total 96 84 180 Perform a x? test, at the 5% level of significance, whether cancer incidence rates differ between the three levels of radiation among phosphate mine workers.

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Exercise 3. Let X be a random variable with mean µ and variance o². For a E R, consider the expectation E((X – a)?). a) Write E((X – a)²) in terms of a, u and o². b) For which value a is E((X – a)²) minimal? c) For the value a from part (b), what is E((X – a)²)?