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    IB Math AAHL
    /
    Distributions & Random Variables
    /

    Video

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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.

    Linear Transformation of Random Variables

    AHL 4.14

    Suppose that the random variable X is scaled and shifted, producing the random variable aX+b. The expected value and variance of the resulting variable are

    E(aX+b)Var(aX+b)​=aE(X)+b=a2Var(X)​📖


    Example

    The continuous random variable X has E(X)=−4 and Var(X)=3. Find the expected value and standard deviation of Y=2X+7.


    E(2X+7)Var(2X+7)​=2E(X)+7=−1=22Var(X)=12​


    So the standard deviation of Y is √12=2√3=3.46

    Linear Transformation of Random Variables

    AHL 4.14

    Suppose that the random variable X is scaled and shifted, producing the random variable aX+b. The expected value and variance of the resulting variable are

    E(aX+b)Var(aX+b)​=aE(X)+b=a2Var(X)​📖


    Example

    The continuous random variable X has E(X)=−4 and Var(X)=3. Find the expected value and standard deviation of Y=2X+7.


    E(2X+7)Var(2X+7)​=2E(X)+7=−1=22Var(X)=12​


    So the standard deviation of Y is √12=2√3=3.46

    HL