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  • Perplex
    IB Math AIHL
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    Distributions & Random Variables
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    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: 7
    63

    0 / 17

    A geometric sequence has first term u1​=34​, fifth term u5​=121​, and common ratio r>0.

    1. Find the value of r.

      [3]

    The following table shows the probability distribution of a random variable X.

    x

    1

    4

    16

    64

    256

    1024

    P(X=x)

    ku1​

    ku2​

    ku3​

    ku4​

    ku5​

    ku6​

    1. Find k, giving your answer as a fraction.

      [5]
    2. Hence determine E(X).

      [4]

    A random variable Y, defined by Y=aX+3, has Var(Y)=3937.

    1. Given that E(Y)=10, find the standard deviation σX​ of X.

      [5]
    64

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