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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.

    Expected Value of a Continuous Random Variable

    AHL 4.14

    The expected value of a continuous random variable is

    E(X)=μ=∫−∞∞​xf(x)dx📖

    Intuitively, this can be thought of as the "balance point" of the distribution, the weighted sum of all values of x.


    The expected value is also known as the mean.


    Example

    The continuous random variable X has the probability density function

    f(x)={2x0​0<x<1otherwise​​

    Find E(X).


    E(X)  ​=∫01​x⋅2xdx=∫01​2x2dx =[32x3​]01​=32​​

    Expected Value of a Continuous Random Variable

    AHL 4.14

    The expected value of a continuous random variable is

    E(X)=μ=∫−∞∞​xf(x)dx📖

    Intuitively, this can be thought of as the "balance point" of the distribution, the weighted sum of all values of x.


    The expected value is also known as the mean.


    Example

    The continuous random variable X has the probability density function

    f(x)={2x0​0<x<1otherwise​​

    Find E(X).


    E(X)  ​=∫01​x⋅2xdx=∫01​2x2dx =[32x3​]01​=32​​
    HL