Question: A random number machine generates random digits between 0 and 9. Each of the ten digits is equally likely to be generated. (a) X is

A random number machine generates random digits between 0 and 9. Each of the ten digits is equally likely to be generated.

(a) X is the value of the digit generated. Find (i) P(X <6), (ii) P(X>7), (iii) E(X), (iv) the standard deviation of X.

(b) X is the number of digits generated to the first occurrence of a 5. Find (i) the probability that the first occurrence of the digit 5 is at the seventh number generated, (ii) the most likely number of digits generated to obtain a 5, (iii) the mean number of digits generated to obtain a 5.

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