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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.

    Median of a Continuous Random Variable

    AHL 4.14

    The median of a continuous random variable X is the value m that splits the distribution into two equal areas:

    ∫−∞m​f(x)dx=∫m∞​f(x)dx=21​🚫

    Powered by Desmos

    Example

    The continuous random variable X has the probability density function

    f(x)=⎩⎪⎨⎪⎧​143​(x2+1) 0​0≤x≤2 otherwise​​


    Find the median m of X.

    143​∫0m​x2+1dx 143​(3x3​+x)0m​ 3m3​+m​=21​ =21​ =37​​

    Using a calculator, we find m=1.41.


    Note that we can avoid doing integrals at all by plotting

    Y1​ Y2​​=143​∫0x​(x2+1)dx =0.5​

    on a calculator and finding the intersection x=1.4062876→m=1.41.

    Median of a Continuous Random Variable

    AHL 4.14

    The median of a continuous random variable X is the value m that splits the distribution into two equal areas:

    ∫−∞m​f(x)dx=∫m∞​f(x)dx=21​🚫

    Powered by Desmos

    Example

    The continuous random variable X has the probability density function

    f(x)=⎩⎪⎨⎪⎧​143​(x2+1) 0​0≤x≤2 otherwise​​


    Find the median m of X.

    143​∫0m​x2+1dx 143​(3x3​+x)0m​ 3m3​+m​=21​ =21​ =37​​

    Using a calculator, we find m=1.41.


    Note that we can avoid doing integrals at all by plotting

    Y1​ Y2​​=143​∫0x​(x2+1)dx =0.5​

    on a calculator and finding the intersection x=1.4062876→m=1.41.

    HL