Question: Let X N(,2). Show that (a) Z = (X) is N(0,1). (b) U = (X)2 2 is 2(1).

Let X ∼ N(μ,σ2). Show that (a) Z = (X−μ) σ is N(0,1). (b) U = (X−μ)2 σ2 is χ2(1).

Step by Step Solution

★★★★★

3.39 Rating (152 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

According to ... View full answer

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 Accounting Questions!

Q:

Let A and B be n x n matrices. Show that if A is similar to B then there exist n x n matrices S and 7, with S nonsingular, such that A = ST and B = TS

Q:

Let z be the n à 1 column vector all of whose entries are equal to 1. (a) Show that if A is an m à n matrix, the ith entry of the product v = Az is the ith row sum of A, meaning the sum...

Q:

Show that if U is an n x n orthogonal matrix then u1uT1 + u2uT2 + + unuTn = I

Q:

MAT314 - Complex Analysis \\x u. I! u. n I I Problem 6. Find the area of the image of D (0, 1) under the map f (z) = z + g Problem 7. Suppose f is holomorphic on D(0, 1). f(0) = 3 + 42' and |f(z)| S...

Q:

Let F be the c.d.f. of a discrete distribution that has the memoryless property stated in Theorem 5.5.5. Define (x) = log[1 F(x 1)] for x = 1, 2, . . .. a. Show that, for all integers t, h > 0, 1...

Q:

Assignment 4: Problem 5 Previous Problem Problem List Next Problem (1 point) A function f is said to have a removable discontinuity at a if: 1. f is either not defined or not continuous at a. 2. f(a)...

Q:

Consider the following simplified scenario based on Who Wants to Be a Millionaire?, a game show in which the contestant answers multiple-choice questions that have 4 choices per question. The...

Q:

Problem 3: Let the set of rational numbers in [0, 1] be denoted by Q = {r1, r2 , . .., rn , . .. }, and define fn(2) =0, if x E {r1, r2, ..., Tn}; fn() =1, if x & {ri,r2, ..., In}. (i) Show that fn...

Q:

Establish the identity (ez)n = enz (n = 0, 1, 2, . . .) in the following way. (a) Use mathematical induction to show that it is valid when n = 0, 1, 2, . . . . (b) Verify it for negative integers n...

Q:

Let f (x) = 0 if x is any rational number and f (x) = 1 if x is any irrational number. Show that f is not integrable on [0, 1].

Q:

Zedan received a telephone call from a Saudi Arabian organization offering him an engineering position at a construction project in Saudi Arabia. The Ministry of Communications, an agency of the...

Q:

The examples of the two previous exercises can be explained in terms of momentum conservation and in terms of Newton's third law. Assuming you've answered them in terms of momentum conservation,...

Q:

Agreements falling within the per se category are tested based on their impact on competitive conditions. They are only illegal if they suppress or destroy competition.TrueFolse

Q:

The Blue Division of Dalby Company reported the following data for the current year. Sales ........ $3,000,000 Variable costs ...... 1,950,000 Controllable fixed costs .. 600,000 Average operating...

Q:

The green division of Campana Company reported the following data for the current year: Sales...........................................$3,000,000 Variable...

Q:

1. Linda Turner will face different challenges as her company progresses through the five stages of growth described in this chapter. Describe how you believe her business would change in each stage....

Q:

Preparing the balance sheet Prepare the balance sheet of Decorating Arrangements as of December 31, 2016. Insurance Expense....... $ 2,000 Service Revenue....... 80,000 Utilities Expense....... 500...

Q:

Preparing the statement of retained earnings Prepare the statement of retained earnings of Decorating Arrangements for the year ended December 31, 2016. Insurance Expense....... $ 2,000 Service...

Q:

Choose the correct answer True or False 0.5 points While common law systems rely on caselaw and legal precedent to guide their decisions, civil law systems rely primarily on codes and statutes. O...

Q:

Let x [n] and y [n] denote complex sequences and X(e j? ) and Y(e j? ) their respective Fourier transforms. (a) By using the convolution theorem (Theorem 6 in Table 2.2) and appropriate properties...

Q:

Consider an N-point sequence x[n] with DFT X[k], k = 0, 1, ?, N ? 1. The following algorithm computes the even-indexed DFT values X[k], k 0 , 2, ?. , N ? 2, for N even, using only a single N/2 ?point...

Q:

In Eq.38-18 keep both terms, putting A - B ? ? 0 the equation then describes the superposition of two matter waves of equal amplitude, traveling in opposite directions. (Recall that this is the...

Q:

Suppose that a finite-length sequence x[n] has the N-point DFT X [k], and suppose that the sequence satisfies the symmetry condition x[n] = x[((n + N/2)) N ], 0 n N 1, where N is even and x [n]...

Q:

The model y1 = 1x1 + 1, y2 = 2x2 + 2 satisfies all the assumptions of the classical multivariate regression model. All variables have zero means. The following sample second-moment matrix is obtained...

Q:

Figure (a) shows charged particles 1 and 2 that are fixed in place on an x axis. Particle t has a charge with a magnitude of |q1| = 8.00e. Particle 3 of charge q3 = + 8.00e is initially on the x axis...