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  • Perplex
    IB Math AAHL
    /
    Distributions & Random Variables
    /

    Problem Bank

    [Maximum mark: 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]

      To earn a crown, get your answer ready before you reveal the options!

    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]

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