Let X be a random variable with the following probability distribution.Value x of X10203040P (X=x)0.300.400.250.05Complete the following. (If necessary, consult a list of formulas.)(a) Find the expectation E (X) of X.E (x) = 0(b) Find the variance Var(x) of X.Var(x) = |

The probability distribution table provided in the question is as follows :-Value x of…

Answered: Complete the following. (If necessary,…

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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In baseball there are many ways to estimate what a team's winning percentage (w) should be against its opponents, given the total runs it has scored and the total runs it has allowed in a certain number of games. Bill James's Pythagorean Formula for the winning percentage estimator is given below. wpe = w = [(# runs scored)2]/[(# runs scored)2 + (# runs allowed)2] A team has currently scored 369 runs and allowed 329 runs. If the team does not allow any more runs for the rest of the season, how many additional runs must they score in order to have a wpe of 80%? (Hint: Let x = the number of runs additional scored.)
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A individual, with a utility function lnW and an initial wealth level W0, is faced with a fair gamble of winning or losing $h (where W0 > h > 0) with 50-50 chance. (a) Is this individual risk averse? Explain.(b) Suppose that the individual is willing to pay up to an amount of f in order to avoid such a gamble. Give the equation that determines f, and solve the equation for f (i.e., express f in terms of W0 and h). (c) Show that f increases as h increases.
3. 1 + x Check whether the following function is a valid pdf? If it is valid, obtain its CDF. If not valid, would scaling by a constant make it valid? If so, make it valid. Obtain its CDF? What is its mean? Variance? ƒ = —exp(-√x)U(x)
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The Lorenz curve of income distribution in a small mountain nation is f(x)=0.5x¹ +0.3x³ +0.2x The Gini coefficient (index) of inequality for this nation is . . . O...y=0.562 O...y=0.513 O...y=0.37 O...y=0.45

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Complete the following. (If necessary, consult a list of formulas.) (a) Find the expectation E (X) of X. E (x) = [ (b) Find the variance Var(X) of X. Var(x) = 0