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One way to generate random numbers in Excel is with the RAND function. By itself, RAND generates a limited range of random numbers, but by using it in formulas with other functions, you can expand the range of values so that:

The random numbers or letters will be the random sample set. For Sample Size enter the value for the number of samples you need. For the Sample Range enter the range of values to randomly choose from. For example, to choose from 1 to 100 enter 1-100; to choose from a through m enter a-m or A-M. If the sample size is greater than the sample.

• RAND can be made to return random numbers within a specified range, such as 1 and 10 or 1 and 100 by specifying the high and low values of a range,
• You can reduce the function's output to integers by combining it with the TRUNC function, which truncates or removes all decimal places from a number.

The RAND function returns an evenly distributed number greater than or equal to 0 and less than 1. While it is normal to describe the range of values generated by the function as being from 0 to 1, in reality, it is more exact to say the range is between 0 and 0.999...

These instructions apply to Excel 2019, 2016, 2013, 2010, Excel Online and Excel for Office 365.

RAND Function Syntax and Arguments

A function's syntax refers to the layout of the function and includes the function's name, brackets, comma separators, and arguments. The syntax for the RAND function is:

Unlike the RANDBETWEEN function, which requires high-end and low-end arguments to be specified, the RAND function accepts no arguments.

You can see several RAND function examples in the above image.

• The first example (row 2) enters the RAND function by itself.
• The second example (rows 3 and 4) creates a formula that generates a random number between 1 and 10 and 1 and 100.
• The third example (row 5) generates a random integer between 1 and 10 using the TRUNC function.
• The last example (row 6) uses the ROUND function to reduce the number of decimal places for random numbers.

Generating Numbers with RAND

Again, since the RAND function takes no arguments, you can enter it by clicking on a cell and typing =RAND() which results in a random number between 0 and 1 in the cell.

The general form of the equation used to generate a random number within a specified range is:

High and Low signify the upper and lower limits of the desired range of numbers. As an example, to generate a random number between 1 and 10 enter the following formula into a worksheet cell:

Generating Random Integers with RAND

To return an integer — a whole number with no decimal portion — the general form of the equation is:

Rather than remove all decimal places with the TRUNC function, we can use the following ROUND function in conjunction with RAND to reduce the number of decimal places in the random number to two.

RAND Function and Volatility

The RAND function is one of Excel's volatile functions; this means that:

• The function recalculatesand produces a new random number every time anyone makes a change to the worksheet, including actions such as adding new data.
• Any formula that depends either directly or indirectly on a cell containing a volatile function also recalculates every time someone makes a change in the worksheet.
• In worksheets or workbooks containing large amounts of data, take caution when using volatile functions because they can slow down the program's response time due to the frequency of recalculations.

You can also force the RAND function to produce new random numbers without making other changes to a worksheet by pressing the F9 key on the keyboard. This action forces the entire sheet to recalculate including any cells containing the RAND function.

You can also use the F9 key to prevent a random number from changing every time someone makes a change to the worksheet:

1. Click on a worksheet cell where you want the random number to reside.

2. Type the function =RAND() into the formula bar above the worksheet.

3. Press the F9 key to change the RAND function into a static random number.

4. Press the Enter key on the keyboard to display the random number into the selected cell.

5. Now, pressing F9 won't affect the random number.

Random Serial Number Generator

Random serial dictatorship (RSD),^[1] also called: random priority (RP),^[2] is a procedure for dividing indivisible items fairly among people.

Suppose ${\displaystyle n}$ partners have to divide ${\displaystyle n}$ (or fewer) different items among them. Since the items are indivisible, some partners will necessarily get the less-preferred items (or no items at all). RSD attempts to insert fairness into this situation in the following way. Draw a random permutation of the agents from the uniform distribution. Then, let them successively choose an object in that order (so the first agent in the ordering gets first pick and so on).

Properties[edit]

RSD is fair, at least in the sense of equal treatment of equals, since each agent has the same chance to appear in each position in the ordering.

RSD is a truthful mechanism when the number of items is at most the number of agents, since you only have one opportunity to pick an item, and the obviously-dominant strategy in this opportunity is just to pick the best available item.

However, RSD is not Pareto efficient when the agents have Von Neumann-Morgenstern utilities over random allocations (lotteries over objects).In fact, there exists no mechanism that satisfies symmetry, truthfulness and Pareto efficiency.^[3]

As an example, suppose there are three agents, three items and the VNM utilities are:

RSD gives a 1/3 chance of every object to each agent (because their preferences over sure objects coincide), and a profile of expected utility vector (0.6, 0.4, 0.4). But assigning item y toAlice for sure and items x,z randomly between Bob and Carl yields the expected utility vector (0.8, 0.5, 0.5). So the original utility vector is not Pareto efficient.^[2]

Random Serial Number

In fact, when the rankings of the agents over the objects are drawn uniformly at random, the probability that the allocation given by RSD is Pareto efficient approaches zero as the number of agents grows.^[4]

Generalization[edit]

RSD can also be defined for the more general setting in which the group has to select a single alternative from a set of alternatives. In this setting, RSD works as follows: First, randomly permute the agents. Starting with the set of all alternatives, ask each agent in the order of the permutation to choose his favorite alternative(s) among the remaining alternatives. If more than one alternative remains after taking the preferences of all agents into account, RSD uniformly randomizes over those alternatives. In the item division setting mentioned earlier, the alternatives correspond to the allocations of items to agents. Each agent has large equivalence classes in his preference, since he is indifferent between all the allocations in which he gets the same item.

In this general setting, if all agents have strict preferences over the alternatives, then RSD reduces to drawing a random agent and choosing the alternative that the agent likes best. This procedure is known as random dictatorship (RD), and is the unique procedure that is efficient and strategyproof when preferences are strict.^[5] When agents can have weak preferences, however, no procedure that extends RD (which includes RSD) satisfies both efficiency and strategyproofness.^[6]

See also[edit]

References[edit]

Random Serial Number Generator

1. ^Abdulkadiroglu, Atila; Sonmez, Tayfun (1998). 'Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems'. Econometrica. 66 (3): 689. doi:10.2307/2998580. JSTOR2998580.
2. ^ ^abBogomolnaia, Anna; Moulin, Hervé (2001). 'A New Solution to the Random Assignment Problem'. Journal of Economic Theory. 100 (2): 295. doi:10.1006/jeth.2000.2710.
3. ^Zhou, Lin (1990). 'On a conjecture by gale about one-sided matching problems'. Journal of Economic Theory. 52: 123. doi:10.1016/0022-0531(90)90070-Z.
4. ^Manea, Mihai (2009). 'Asymptotic ordinal inefficiency of random serial dictatorship'. Theoretical Economics. 4 (2): 165–197.
5. ^Gibbard, Allan (1977). 'Manipulation of schemes that mix voting with chance'. Econometrica. 45 (3): 665–681.
6. ^Brandl, Florian; Brandt, Felix; Suksompong, Warut (2016). 'The impossibility of extending random dictatorship to weak preferences'. Economics Letters. 141: 44–47. arXiv:1510.07424. doi:10.1016/j.econlet.2016.01.028.

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