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## Let X be a random day of the week, coded so that Monday is 1, Tuesday is 2, etc. (so X takes values 1, 2,…, 7, with equal probabilities).

Question

Let X be a random day of the week, coded so that Monday is 1, Tuesday is 2, etc. (so X takes values 1, 2,…, 7, with equal probabilities). Let Y be the next day after X (again represented as an integer between 1 and 7). Do X and Y have the same distribution

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2021-09-11T00:21:52+00:00
2021-09-11T00:21:52+00:00 1 Answer
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## Answers ( )

Answer:Yes. Have the same distribution.

Step-by-step explanation:Given that X is a random day of the week, coded so that Monday is 1, Tuesday is 2, etc. (so X takes values 1, 2,…, 7, with equal probabilities).

Y is the next day after X

So Y can be written as X+1

But since highest value is 7, we can write

Y = X+1 mod 7

i.e. whenever X=7, Y= 8= 1 again.

Thus Y can take values as

Y 1 2 3 4 5 6 7

P(Y) = P(X+1) = 1/7

i.e. Y also has the same distribution as X