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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Maria 1 week 2021-09-11T00:21:52+00:00 1 Answer 0

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    2021-09-11T00:23:17+00:00

    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

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