Question: Suppose that X Exp(1), let Y be the integer part and Z the fractional part, that is, let Y = [X] and Z = X

Suppose that X Exp(1), let Y be the integer part and Z the fractional part, that is, let Y = [X] and Z = X [X]. Show that Y and Z are independent and find their distributions.

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!

Detail Instructions and Grading Policies: Each group needs to submit one excel report using the template in the case study 1 posted on Canvas. Please change the names under "Prepared By", "Reviewed...

c) Alternative proof of patterns using ordp. Let ordp(n) define the largest power d such that p divides n. For every real number z, let Lx] denote the integer part of a and {z) := x-laj denote the...

Show workings Kindly. 2. Suppose 42% of Ph.D.s in statistics/biostatistics are earned by woman and a random sample 36 statistics/iostatistics Ph.D.s is obtained.(You may want to use technology to...

M300 Section 201 Assignement 4 due Thursday, February 25 at the beginning of class In this homework, log may be either the multi-valued logarithm or one of its branches: we specify which one for each...

49. Let R and S be rings. a. Show that the mapping from R O S onto R given by (a, b) -> a is a ring homomorphism. b. Show that the mapping from R to R O S given by a -> (a, 0) is a one-to-one ring...

Please ASAP and start from e Problem 5 Here, we will be deriving mof's of some of our brand name r.v.'s and using them to prove cool things about distribution theory. (a) [harder] Using the...

please help Find all the values of x such that the given series would converge. 00 9331?, 2() 11:1 The series is convergent from m = [j , left end included (enter Y or N): to a: = C] , right end...

can someone pls help with this differential geometry q with full method. thanks x (4) [Marked] Let S denote the surface S={(x, y, z) ER3|(1 + x2)2 = y2 +z?, x (0,1)). (S is a "surface of revolution",...

Show that the distribution of Z may be approximated by a normal distribution for any large, not necessary integer, . (Advice: First, = []+{}, where [] is the integer part of , and {}=[], the...

The attachment of the N-protected C-terminal amino acid to the polymer in solid-phase peptide synthesis (Figure 17.7) is an SN2 displacement reaction. What is the nucleophile? What is the leaving...

The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance follows Payment ($) Probability 0 ............85 500 ............04 1000...

Which pair contains two common control accounts? Accounts receivable and equipment. Accounts receivable and common stock. Accounts receivable and accounts payable. Equipment subsidiary ledger and...

Assuming the data are normal, what is the probability the blade weights from this process will exceed 5.20? What is the probability that weights will be less than 4.80? What is the actual percent of...

Hank has a 30% interest in KKC LLC, a calendar year entity. At the beginning of the year, Hank had an outside basis in KKC of $60,000 which included his $10,000 share of KKC liabilities. On July 1st,...

Redang Chalet Sdn Bhd (RCSB) rents out chalet to tourists at a popular beach in Redang, Terengganu. RCSB own 10 chalets, in which the construction cost amounted to RM1 million. Each chalet is...

Reba Dixon is a fifth-grade school teacher who earned a salary of $38,000 in 2019. She is 45 years old and has been divorced for four years. She receives $1,200 of alimony payments each month from...

You have been hired by Gnomeo, Inc., a company that buys and resells miniature garden gnomes. The company started business on January 1, 2019. The chief accountant has asked you to compile a set of...

Among a group of 5 8 programmers, who know either Java or Python or both, 1 5 only know Java and 1 3 only know Python. What is the probability of randomly choosing a programmer who knows both...

An improvement in the exchange of information in negotiations.

1. Effort is important.

2. Set up two points representing the pillars of your values system. Discuss this with the others in the group.