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Distribution table with entries k, 2k, ...: find k, then P(1 < X < 4 given X <= 2)

The same question, asked 2 times: 2021 Paper 21*, 14 Jun 2022. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 21

    83
    The probability distribution of random variable XX is given by:
    XX12345
    P(X)P(X)KK2K2K2K2K3K3KKK
    Let p=P(1<X<4∣X<3)p = P(1 < X < 4 \mid X < 3). If 5p=λK5p =\lambda K, then λ\lambda equal to

  2. Question 2

    14 Jun 2022

    162
    A random variable XX has the following probability distribution:
    XX01234
    P(X)P(X)kk2k2k4k4k6k6k8k8k
    The value of P(1<X<4∣X≤2)P(1 < X < 4 \mid X \leq 2) is equal to:

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