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X equally likely on 1, 2, ..., n with a given Var(X) : E(X): find n

The same question, asked 2 times: 10 May 2023 S2*, 9 May 2024 S2. Every wording below, oldest first.

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  1. Question 1

    10 May 2023 S2

    123
    A random variable X assumes values 1,2,3,…,n1, 2, 3, \ldots, n with equal probabilities. If Var(X):E(X)=4:1\text{Var}(X) : E(X) = 4 : 1, then n is equal to

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  2. Question 2

    9 May 2024 S2

    148
    A random variable X assumes values 1,2,3,…,n1,2,3,\ldots,n with equal probabilities, if Var(X)=E(X)\text{Var}(X) = E(X), then nn is

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