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Probability table with linear multiples of k: find k, then a probability

This type of question, asked 5 times: 3 May 2023 S1, 19 Apr 2025 S1, 20 Apr 2025 S1, 25 Apr 2025 S1, 15 May 2026 S2. All 5 questions below, oldest first.

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  1. Question 1

    3 May 2023 S1

    109
    A random variable X has the following probability distribution. Then value of k is___ and P(3<x≤6)P(3<x\leq6) has the value. \begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline X=x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8\\ \hline P(x) & k & 2k & 3k & 4k & 4k & 3k & 2k & k & k\\ \hline\end{array}

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  2. Question 2

    19 Apr 2025 S1

    115
    The probability distribution of a discrete random variable X is
    XX01234
    P(X=x)P(X = x)2k2kkk2k2k4k4kkk
    If a=P(x<3)a = P(x< 3) and b=P(2≤X<4)b = P(2 \leq X < 4), then

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  3. Question 3

    20 Apr 2025 S1

    120
    A random variable XX has the following probability distribution
    XX01234
    P(X)P(X)kk2k2k4k4k2k2kkk
    then the value of P(1⩽X<4∣X⩽2)=P(1 \leqslant X< 4 \mid X\leqslant 2) =

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  4. Question 4

    25 Apr 2025 S1

    116
    Let X denote the number of hours you study on a Sunday. It is known that P(X=x)={0.1, if x=0kx, if x=1 or 2k(5−x), if x=3 or 40, otherwise P(X =x) =\left\{ \begin{matrix} 0.1 & ,\text{~if~}x= 0 \\ kx & ,\text{~if~}x= 1\text{~or~}2 \\ k(5 -x) & ,\text{~if~}x= 3\text{~or~}4 \\ 0 & ,\text{~otherwise~} \end{matrix} \right.where k is constant. Then the probability that you study at least two hours on a Sunday is

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  5. Question 5

    15 May 2026 S2

    99
    The probability distribution of a discrete random variable (r.v.) XX is given below:
    X=xX = x0011223344
    P(X=x)P(X = x)kk2k2k4k4k2k2kkk
    Then the value of P[X≤E(X)]P[X \le E(X)] is:

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