Question: Let X N(, 2). Consider the function g : R R defined by g(t) = E[(X t)^2], t R. Show that the function g attains

Let X N(, 2). Consider the function g : R R defined by g(t) = E[(X t)^2], t R. Show that the function g attains its minimum value on R at the point t0 E(X)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

2. Consider the function f : R - R defined by f (2) = (10 sin(x), 23) (a) Prove that f is injective. You may assume that the function g : R - R defined by g(x) = x is injective, but you should state...

How to solve these 3 different questions? ( 2 marks ) Consider the function f : R > IR defined by an) = 4a: +8taII1 at. First let us evaluate f(1) (in the exact form). f(1)= -42*Pi o n E . Let us...

(1) Consider the following system of linear equations 3x + 2y + 203 = -13 -5 5x + 2ay - 3: = -18 where a E R is a constant. (a) Classify the system according to the values of a b) Solve the above...

please help 5. For a function f : A - B and subsets E and F of B, prove f-'(E - F) = f-'(E) -f-'(F). 6. Let f : R - R be the function defined by f(x) = x2 + ax + b, where a, be R. Determine whether f...

+ Let (X, : n 2 1) be an infinite sequence of random variables. For each n, we denote the density function for X, by fx,, : IR - R. Consider the following statements: of Statement A: If fx, (x ) = 2n...

L Let n be an integer, n > 1. Consider the function g defined by ( acy 2 ) n g(x, y) = 2 2 + 2/2 , if (x, y) + (0,0) ; 0 , if (x, y) = (0,0) . (a) [ | mark -) Using the principal definition of...

TMA4140 DISCRETE MATHEMATICS NTNU, H2022 (2) Consider the function f : R - R, x -> f(2) = 12 -3x+2 (a so-called quadratic polynomial). i) Is f injective, surjective, or both? ii) Is f : R - [-0.25,...

1. Based on data from the US Census Bureau, the US population in 1990 was approximately 250 million people and in 2000 was approximately 280 million people. Assume an exponential growth model for the...

Let X = R 2 +. The lexicographic preference relation L is defined as x L y if either x1 > y1 or x1 = y1 and x2 y2. The name derives from the way a dictionary is organized; that is commodity 1 has the...

Consider the function g : R^3 ? R defined by g(x, y, z) = x^2 + 2y^2 ? z^a , where the natural number a satisfies a ? 2 (a) Show that for all e 2 2, the point (0,0,0) is the only stationary point of...

Financial and non-financial performance measures, goal congruence. (CMA, adapted) Summit Equipment specializes in the manufacture of medical equipment, a field that has become increasingly...

Using the graph of x versus t in Figure, find (a) The average velocity for the time intervals t = t 2 0.75 s when t 2 is 1.75, 1.5, 1.25, and 1.0s; (b) The instantaneous velocity at t = 0.75 s; (c)...

What is the forward premium of the Brazilian real if the Argentinean peso trades at 2 . 4 8 3 7 % forward discount against it ?

8:37 * N. 80% i ... OBJECTIVES: Create relationships Create a Pivot Table from Related Tables Create a PivotChart Modify the PivotChart The major section in this chapter :ontinuation is: Data...