Let X be a random variable. Suppose we try to use a constant real number â to guessthe value of X. Let E(X – î)² be the mean squared error (MSE) of this estimation.(i) By writing X − â = (X − E X) + (EX − 2), show thatE(X)² = Var(X) + (EX - 2)².=(ii) Conclude that the MSE is minimized for îVar(X).EX and the minimum MSE equals to

Answered: Image /qna-images/answer/e99450f5-11d2-4ca9-a056-55590820cf38.jpg

Answered: Let X be a random variable. Suppose we…

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...

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A medical researcher says that less than 82% of adults in a certain country think that healthy children should be required to be vaccinated. In a randon sample of 300 adults in that country, 78% think that healthy children should be required to be vaccinated. At a = 0.10, is there enough evidence to support the researcher's claim? Complete parts (a) through (e) below. (a) Identify the claim and state Ho and Ha Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) CA. Less than 82 % of adults in the country think that healthy children should be required to be vaccinated. O B. The percentage of adults in the country who think that healthy children should be required to be vaccinated is not %. O C. More than % of adults in the country think that healthy children should be required to be vaccinated. O D. % of adults in the country think that healthy children should be required…
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
Farmers face uncertainty over their earnings because rain is random. Let a farmer's yield be Y= 0 in the dry outcome and Y = 1 in the wet outcome. However, not all farmers are the same: Probability(Y= 1) = p1= 2/ 3 if type = 1 p0= 1/ 3 if type = 0 All farmers are risk averse, with utility U(Y) = √Y as their utility function. Farmers know their type. (a) Calculate each farmer's expected yield, E(Yi) =pI1 + (1- pi)0, expected utility ,E(Ui) =piU(1) + (1 - pi)U(0), and calculate the utility at E(Yi), U(E(Yi)), for i= 0, 1. Show these all on a graph with utility on the vertical axis and yield on the horizontal axis.
With an American penny, the likelihood of getting H when it is spun on edge is 0.3. If X is the random variable where X(H ) = 1, X(T ) = −1, find the expected value E(X), the variance, Var(X), and express X in its standard form.
The expected value of the sum or difference of two or more functions of a random variable X is the sum or difference of the expected values of the functions. That is, E[g(X)±h(X)] = E[g(X)] ± E[h(X)].
If the odds against T occurring are 8:5, then find P(T) and P(T'). P(T) = (Simplify your answer.) P(T') = (Simplify your answer.)
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1. Suppose that the PDF of X is given by 1+0.4x2 0< x <1 f(x) otherwise a. Find the expected value of X, E(X). b. Find the variance of X, Var(X). c. Find the standard deviation of X, Std(X)
Let X ~ F(a, ß). If E(X)= % and E(X²)= a+a² If â = nX? find the method of (n-1)s² | .3 moments estimator of
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.
2.11 Let X have the standard normal pdf, fx(x) = (1/√√2π) e¯2²/² (a) Find EX² directly, and then by using the pdf of Y = X2 from Example 2.1.7 and calculating EY. (b) Find the pdf of Y = |X|, and find its mean and variance.
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