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  • Perplex
    IB Math AIHL
    /
    Distributions & Random Variables
    /

    Problems

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    Problem Bank - Distributions & Random Variables

    Access custom-built, exam-style problems for distributions & random variables. Each problem has a full solution and mark-scheme, as well as AI grading and support.

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    IB: 5
    8

    0 / 9

    The following diagram shows the curve of the normal distribution of the random variable X.

    Powered by Desmos

    The area of the shaded region R is 0.32.

    1. Find the value of P(X<92).

      [1]

    It is given that P(X>58)=0.68.

    1. Find the expected value, μ, of X.

      [2]
    2. Determine the value of

      1. P(58<X<μ),

        [2]
      2. P(58<X<92∣X<92)

        [4]
    9

    0 / 6

    The probability distribution of a discrete random variable X is shown in the following table.

    x

    1

    2

    3

    4

    5

    P(X=x)

    0.1

    4(2p−3)2​

    0.2

    0.2

    46p−11​

    Find the possible value(s) of p.

    [6]
    10

    0 / 13

    At a local carnival, players can pay 6 tokens to play Lucky Spinner. Each turn, the player spins a wheel with segments numbered 0-4. If the wheel lands on s, the player wins s2 tokens.


    The following table shows the distribution S of spins s.


    s

    0

    1

    2

    3

    4

    P(S=s)

    0.1

    0.2a

    0.3

    a

    b


    It is given that the game is fair.

    1. Show that a=2512​.

      [5]
    2. Find the value of b.

      [1]

    Let L∼B(5,p) be the random variable representing the number times a player loses money in 5 turns.

    1. Show that p=12562​.

      [1]
    2. Find the variance of L, giving your answer to 4 decimal places.

      [2]
    3. Given that Elise lost money on at least 3 of her 5 turns, find the probability she lost money every time.

      [4]
    11

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