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Use the row of numbers shown below to generate 12 random numbers between 01 and 99. 78038 18022 84755 23146 12720 70910 49732 79606 Starting at the beginning of the row, what are the first 12 numbers between 01 and 99 in the sample?

This problem aims to find a bunch of random numbers from a row of numerical values. The main concept behind this problem is mostly related to random numbers and their generation. Now as the phrase suggests, a random number is just a number chosen by luck. In a random number distribution, all the numbers have an equal probability of being selected randomly. For instance, choosing a random card from a deck of $52$ cards.

A random number appears in a particular distribution solely when two requirements are met, the first one is that the numbers should be uniformly dispersed, secondly, it should be impossible to foretell future numbers.

If we want a number in a row or distribution to be actually random, the number must be independent of the row. This means that there is no conncetion between consecutive numbers.

Expert Answer

True random numerals are mostly derived from a set of unit decimal numbers such as $0,1,2,3,…,7,8,9$. Before answering this problem, we will use the row distribution to write down the given numbers.

\[78038, 18022, 84755, 23146, 12720, 70910, 49732, 79606 \]

So we have a cluster of numbers, arranging them in pairs of $5$, starting from $78038$ followed by $18022$ then $84755$ and then $23146$ and then $12720$ followed by $70910$ followed by $49732$ and lastly the row ends at $79606$.

Now that the distribution is all lined up and the sequence is maintained, we will now focus on our purpose for this problem to randomly select $12$ numbers from $0$ to $99$ using the above distribution.

Since $99$ is a two-digit numerical value, we will take two digits for each of our random numbers as we go along the sequence. So we’ll carry these two numbers and we get the digit $78$ and then we assume the next two digits and we get the number $03$. One thing to keep in view is the space, but don’t worry about it.

So we get the number $81$ and we will continue this until we gain a total of $12$ distinctive numbers. Hence, we get $80$, then $22$, and then using the same technique we will get, $84, 75, 52, 31, 46, 12$ and $72$. Now, if any of the digits were duplicated, we would just dump that number, and resume until we get $12$ distinctive numbers.

Numerical Result

The random numbers are $78, 03, 81, 80, 22, 84, 75, 52, 31, 46, 12, 72$.

Example

Use the row below to generate $12$ random numbers that are sampled between $0$ and $99$.

$89451, 26594, 02154, 03265, 01548, 65210, 78410, 56410$.

Since $99$ is comprised of two digits, we take two digits for each random number. We get the digit $89$ and then we get the number $45$ and then we take the next two digits.

So we get the number $12$ and we will continue to get $65$, then we’d get $94$, and then using the same technique, we will get $02, 15, 40, 32, 65, 01$ and $54$.

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