Which of the following statements are true of a table of...

Which of the following statements are true of a table of random digits, and which are false? Bricfly explain your answers. (a) There are exactly four 0 s in each row of 40 digits. (b) each pair of digits has chance $1 / 100$ of being 00 . (c) Ilie digits 0000 can never appear as a group, because this pattern is not random.

Which of the following statements are true of a table of random digits, and which are false? Bricfly explain your answers.
(a) There are exactly four 0 s in each row of 40 digits.
(b) each pair of digits has chance $1 / 100$ of being 00 .
(c) Ilie digits 0000 can never appear as a group, because this pattern is not random.

Key Concepts

Expected Frequency Versus Guaranteed Counts

The idea of expected frequency relates to the average number of times a particular digit or group of digits appears over many trials. Although you might expect, say, about four 0s in a row of 40 digits on average, this is not a guaranteed count in every row; probability distributions yield variability around the expected value.

Probability of Specific Digit Patterns

Calculating the chance for a specific pattern, such as a pair of digits being '00', involves multiplying the probability of each digit occurring. With a uniform distribution and independence, the probability of '00' is (1/10)*(1/10) = 1/100. Similarly, this reasoning applies to longer sequences like '0000', which, while having a small probability, can still appear in a truly random sequence.

Uniform Distribution of Digits

A table of random digits generally assumes that every digit (0–9) has the same chance of appearing, which means each digit is selected from a uniform distribution. This concept underpins any discussion about the likelihood of specific digits or patterns occurring in the table.

Statistical Independence

In random digit generation, each digit is produced independently of the others. This means the occurrence of a digit in one position does not affect the probability of any digit occurring in another position. This is key to understanding why, for instance, certain sequences or patterns are possible even if they seem non-random.

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