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My textbook has these following examples of random variables, and I have marked them as discrete and continuous like below. Can someone confirm/contradict with reason, if my understanding is correct?

"In an experiment involving the transmission of a message, (a) the time needed to transmit the message, (b) the number of symbols received in error, and (c) the delay with which the message is received are all random variables."

Here (a) and (c) are continuous random variables and (b) is a discrete random variable, as its values are countably infinite.

Monalisha Bhowmik
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    Do you know the difference between countable and uncountable sets? – K.defaoite Jan 02 '21 at 05:37
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    I think that while part $b$ is definitely discrete for the reason you mention, the time and the delay can be modeled as discrete variables as well, for example they could be represented by (shifted, to avoid zero time) Poisson random variables? Having said that, I think the answer is still correct because they can be modeled as continuous random variables as well. – Sarvesh Ravichandran Iyer Jan 02 '21 at 05:50
  • @K.defaoite : Yes, something flowing continuously can't be counted, so uncountable. E.g. real numbers, time etc. Whereas, like integers, 1,2,3,.... are discrete and countable, but infinite. – Monalisha Bhowmik Jan 02 '21 at 07:19
  • @Teresa Lisbon: Got it. Like e.g. if someone it noting down the time or delay, then those noted down times are also discrete. – Monalisha Bhowmik Jan 02 '21 at 07:21
  • @MonalishaBhowmik Right : but I think your answer will be given as correct for the "flowing continuously" logic that you provide to K.defaoite. – Sarvesh Ravichandran Iyer Jan 02 '21 at 07:22

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