Unif Property Management

Unif Property Management – 0.56 0. 26 0. 96 0. 09 0. 11 0. 85 0. 59 0. 77 0. 93 0. 600. 71 0. 38 0. 49 0. 18 0. 91 0. 62 0. 41 0. 70 0.11 0.45

How many runs up and down do you get from this sequence Solution: Using the usual notation of class, we have the sequence + and the following: + + + + + + + + + This corresponds to A = 16 runs. 13. Referring to Problem 12, perform a run up and down test on the PRN sequence to determine whether it is independent or not. Use = 0. Do you accept or reject independence? Solution: With class records, under the null hypothesis of independence, A Nor(2n−13, 16n−2990) Nor(13, 3). So, the test statistic is Z0=A E[A]qVar(A)=16 13 3= 1.668 |Z0| > zα/2=

Unif Property Management

Unif Property Management

Solution: Consider X1, X2, … , Xni.i. with c.d. F(x) and let t Y max. Then (as finally explained in class) c.d. of Y is G(y) = Pr(Y y)= Pr(max y)= Pr(X1≤ y, X2≤ y, … , Xn≤ y)= [Pr(X1≤ y)]n (because yhe Xi is i.i.)= [F(y) ]n. Now, with the Inverse Transform, G(Y ) = U Unif(0, 1) , and [F (Y )]n= U. Because c.d. from X obviously, F(x) = x2 for 0 < x < 1, we have [Y2]n= Y8= U, so Y = U1/8. 32. Consider the covariance matrix 2 × 2 = 3 22 3!. Find the bottom tria n gu l a r mat r i xC such that CC′= . Solution: This may be a bit of an exaggeration, but the following algorithm (of class) calculates the k × k matrix C:For i = 1, … , k, For j = 1, … , i 1, cij← ij−Pj− 1 =1ciℓcjℓ /cjjcji←

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8cii← ii−Pi−1ℓ=1c2iℓ 1/ We just need to substitute k = 2, 11= 22= 3, and 12= 2 and run the algorithm. For the case i = 1, the loop “For j = 1, … , i 1” becomes “For j = 1 , 0”, and is not executed. So, for this case, we jump to the last task and setc11← 11−0Xℓ=1c21ℓ!1/2= 1/211=√3 this result in hand, we can go to case i = 2. Now loop “For j = 1, … , i−1” becomes “For j = 1”, and we can proceed with the following task: cij= c21← 21−P0ℓ=1ciℓc1ℓ /c11= 21/c11= 2/√3 = 1.1547 = c12← 0and then the final assignment: cii= c22← 22−1Xℓ=1c22ℓ!1/2= 22− c 1/2=3 431/2= 1 91 0 .So after all this, here is our final matrix:C = 3 02/√3q5/3 = 1. 01 1!.(As a check mark, you will see that CC′= , as desired.) Or, if you remember from class noting that C must be a lower triangular matrix, then you can solve CC′= c110c21c22! c11c210 c22!= c211c11c21c11c21c221c222!= 3 22 3!= to get the same answer as before.

1. TRUE or FALSE? It is possible to GET and REMOVE specific E members from a resource pool.

2. TRUE or FALSE? The entity is trying to be in the ANTRIAN Arena block that has fulfilled its capacity

6. What Arena variable would you use to determine how many customers happen to be in a place?

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7. TRUE or FALSE? In Arena, the expression on UNIF(0, 1) + UNIF(0, 1) has the same distribution as

8. YES or NO? Is the generation linear congruence or Xi+1 = (3 XI 5)mod(8) full period?

If X0= 1, then we have X1= 6, X 2= 5, X3= 2, and X4 = 1, so the cycle is after 4 PRNs.

Unif Property Management

9. Again consider the generator Xi+1 = (3 Xi− 5)mod(8). Using X0= 1, calculate PRN U123.

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Solution: With the previous question, we have X123= X119= X3= 2, so U123= 0.2 5.

10. Consider our desert island d gen er a to r Xi+1 = 1 680 7 Ximod(231− 1). If X0=98 76543, find the first

Solution: Either way (for example, with the algorithm given in the note), we find that X1=

11. TRUE or FALSE? There is a perfectly uniform random number generator out there which is NUMBER OUTSIDE MEAT® STOCK MERGERED UNDER DELAWARE STATE LAW SEE THE INVERSE SIDE TO CUSIP’S PARTICULAR DEFINITIONS CUSIP 08862E 10 9 THIS CERTIFICATE THAT

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Can be transferred in the books of the Corporation by the holder directly or by the competent authority after the submission of this certificate which is properly ratified. This certificate is not valid until it is signed and registered by the Transfer Agent and Registrar. IN WITNESS WHEREOF, the Corporation has caused this certificate to be signed with a facsimile signature of the competent authority. Dated:

/s/not legible HEAD OF FINANCE, AGENCY AND SECRETARY /s/not legible CHIEF EXECUTIVE OFFICER AND PRESIDENT SIGNING AND REGISTERING: EQUINITI TRUST COMPANY TRANSFER AGENTS AND REGISTRATION BY AUTHORITIZED SIGNATURE

The Corporation will provide at no cost to any shareholder requesting a statement regarding the relative powers, designations, preferences and rights, participation, optional or other special rights of any class of the Corporation’s shares or series thereof and the qualifications, limitations or limitations of such preferences and/or rights. . The request must be submitted to the Corporate Secretary at the main office of the Corporation. SET THIS CERTIFICATE IN A SAFE PLACE. IF LOST, STOLEN OR DESTROYED, THE COMPANY WILL REQUIRE AN INDEMNITY OF THE BOND AS A CONDITION OF ISSUING A SUBSTITUTE CERTIFICATE. The following abbreviations, when used as written on the face of this certificate, will be interpreted as if they were written in full according to the applicable laws or regulations: SEPULUH COM – as a tenant in general TEN THT – as a tenant as a whole JT TEN – as a joint tenant with the right to survive and not as a tenant in the same COM PROP – as belonging to the UNIF GIFT MIN ACT community ________________ Custodian ______________ (Cust) (Minor) under the Uniform Gifts to Minors Act ____________ (State) UNIF TRF MIN ACT _____________ Custodian ( until the age of _________) (Customer) ______ under the Uniform Transfers (Minor) to Minors Act ____________ (State) Additional abbreviations may also be used even if they are not listed above.

Unif Property Management

PLEASE ENTER SOCIAL SECURITY OR OTHER IDENTIFICATION NUMBER OR RECIPIENT ________________________________________________________________________________________________________(PLEASE PRINT OR WRITE THE NAME AND ADDRESS INCLUDING THE ZIP CODE OF THE RECIPIENT) ___________________________________________________________________________________________________________________________________________________

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The share capital shares represented in the Certificate, hereby irrevocably constitute and designate the _____________________________________________________________________________ power to transfer such shares in the books of the Company in the name with full force of substitution in place. Dated

THIS ASSIGNMENT MARK MUST MATCH THE NAME WRITTEN ON THE FACE OF THE CERTIFICATE IN EACH SPECIAL WITHOUT CHANGING OR ENLARGEMENT OR CHANGING ANYTHING. SIGNATURE GUARANTEED ALL WARRANTIES SHOULD BE MADE BY FINANCIAL INSTITUTIONS (SUCH AS A BANK OR BROKER) THAT IS A PARTICIPANT IN THE SECURITIES TRANSFER AGENT MEDALLION PROGRAM (“STAMP”), THE NEW YORK SIGNAPS MEDALLION STOCK EXCHANGE (“STOCK EXCHANGE”) PROGRAM STOCK EXCHANGE (“SEMP”) AND DOES NOT HAVE TO DATE. WARRANTIES BY THE PUBLIC NOTORY ARE NOT ACCEPTED. In probability theory and statistics, continuous uniform distributions or rectangular distributions are a family of symmetrical probability distributions. The distribution describes an experiment in which there are arbitrary results that lie between certain limits.

The limit is defined by the parameters, a and b, which are the minimum and maximum values. The interval can be closed (eg [a, b]) or op (eg (a, b)).

The difference between the limits defines the lgth interval; all intervals with the same lgth on the distribution support have the same probability. This is the maximum trophy probability distribution for the random variable X under any constraints other than those contained in the distribution support.

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The value of f(x) at the two boundaries a and b is usually unimportant because it does not change the integral value of f(x) dx at any interval, nor x f(x) dx or higher points. Sometimes chos becomes zero, and sometimes chos becomes 1 / b a . The latter is appropriate in the context of estimation by the maximum likelihood method. In the context of Fourier analysis, one can take the value of f(a) or f(b) to be 1/2(b a) , because the inverse transformation of many integral transformations of this uniform function will return the function itself, not the same function “almost everywhere”, i.e. except for a set of points of size zero. Also, it conforms to the sign function which has no such ambiguity.

Graphically, the probability density function is represented as a rectangle where b a is the base and 1 b a }} is the height. As the distance between a and b increases, the dsity at any given value within the boundaries of the distribution decreases.

Since the probability density function is integrated into

Unif Property Management

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