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    IB Math AAHL
    /
    Distributions & Random Variables
    /

    Video

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    Watch comprehensive video reviews for most units, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.

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    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

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    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Distributions & Random Variables

    Video Reviews

    Watch comprehensive video reviews for Distributions & Random Variables, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    HL

    The video will automatically pause when it reaches a problem.

    Variance & SD of discrete variable

    AHL 4.14

    The variance of a discrete random variable can calculated using the formula

    Var(X)  ​=∑(x−μ)2P(X=x)📖=∑x2P(X=x)−μ2📖​


    Example

    The probability distribution of X is shown in the following table:

    x

    1

    2

    3

    P(X=x)

    0.1

    0.5

    0.4

    Find Var(X).


    First, not that we found μ=E(X)=2.3 earlier. Then

    Var(X)  ​=∑x2P(X=x)−μ2 =12⋅0.1+22⋅0.5+32⋅0.4−2.32=0.41​

    Variance & SD of discrete variable

    AHL 4.14

    The variance of a discrete random variable can calculated using the formula

    Var(X)  ​=∑(x−μ)2P(X=x)📖=∑x2P(X=x)−μ2📖​


    Example

    The probability distribution of X is shown in the following table:

    x

    1

    2

    3

    P(X=x)

    0.1

    0.5

    0.4

    Find Var(X).


    First, not that we found μ=E(X)=2.3 earlier. Then

    Var(X)  ​=∑x2P(X=x)−μ2 =12⋅0.1+22⋅0.5+32⋅0.4−2.32=0.41​
    HL