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Statistics / Fundamentals of Probability, with Stochastic Processes 3 / Chapter 7.3 / Problem 12

Fundamentals of Probability, with Stochastic Processes | 3rd Edition | ISBN: 9780131453401 | Authors: Saeed Ghahramani

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QUESTION:

In data communication, messages are usually combinations of characters, and each character consists of a number of bits. A bit is the smallest unit of information and is either 1 or 0. Suppose that L, the length of a character (in bits) is a geometric random variable with parameter p. If a sender emits messages at the rate of 1000 bits per second, what is the distribution of T , the time it takes the sender to emit a character?

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QUESTION:

In data communication, messages are usually combinations of characters, and each character consists of a number of bits. A bit is the smallest unit of information and is either 1 or 0. Suppose that L, the length of a character (in bits) is a geometric random variable with parameter p. If a sender emits messages at the rate of 1000 bits per second, what is the distribution of T , the time it takes the sender to emit a character?

ANSWER:

Step 1 of 5

Consider be the length of a character (in bits), this random variable is a geometric random variable with parameter .

The probability mass function of is given by

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