Problem 7: Let X be a continuous random variable with the probability density f(x) = 3x2 for values ofx in [0,1], and f(x) = 0 elsewhere. Compute the expected value and variance of X.%3D

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Answered: Problem 7: Let X be a continuous random…

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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The probability density function of a discrete random variable X is given by the following table: Px(X = 1) = .05 Px(X = 2) = .10 Px(X = 3) = .12 Px(X = 4) = .30 Px (X = 5) = .30 Px (X = 6) = .1i Px (X = 7) = .01 Px(X = 8) = .01 i) Compute E(X). ii) Compute Var(X). iii) Compute Px(X 3)
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…
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Let X be a Gaussian RV on with expected value (mean) E[X] = 1, Var[X] = 1. Let Y = -3(X-1). Compute the expected value of Y. QUESTION 7 Let X be a Gaussian RV on with expected value (mean) E[X] = 1, Var[X] = 1. Let Y = -3(X-1). Compute the variance of Y.

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Problem 7: Let X be a continuous random variable with the probability density f(x) = 3x2 for values of x in [0,1], and f(x) = 0 elsewhere. Compute the expected value and variance of X. %3D