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    IB Math AAHL
    /
    Distributions & Random Variables
    /

    Video

    Video Reviews

    Watch comprehensive video reviews for most units, 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.

    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 a Continuous Random Variable

    AHL 4.14

    The variance of a continuous random variable X is given by

    Var(X)  ​=E[(X−μ)2]=E(X2)−[E(X)]2📖 =∫−∞∞​x2f(x)dx−μ2📖​


    The standard deviation an be found by taking the square root of this result.


    Example

    The continuous random variable X has the probability density function

    f(x)=⎩⎪⎨⎪⎧​23​x2 0​−1≤x≤1 otherwise​​


    Var(X)=∫−∞∞​x2f(x)dx−μ2


    and μ is clearly zero since 23​x2 is even. So:

    Var(X)=23​∫−11​x4dx=23​⋅52​=53​


    So the standard deviation is √53​​=0.775.

    Variance & SD a Continuous Random Variable

    AHL 4.14

    The variance of a continuous random variable X is given by

    Var(X)  ​=E[(X−μ)2]=E(X2)−[E(X)]2📖 =∫−∞∞​x2f(x)dx−μ2📖​


    The standard deviation an be found by taking the square root of this result.


    Example

    The continuous random variable X has the probability density function

    f(x)=⎩⎪⎨⎪⎧​23​x2 0​−1≤x≤1 otherwise​​


    Var(X)=∫−∞∞​x2f(x)dx−μ2


    and μ is clearly zero since 23​x2 is even. So:

    Var(X)=23​∫−11​x4dx=23​⋅52​=53​


    So the standard deviation is √53​​=0.775.

    HL