Continuous Probability and Geometric Probability Previous Year Questions (PYQs) for GATE DA: 1+ Solved Questions with Step-by-Step Solutions

    Solve 1+ Continuous Probability and Geometric Probability previous year questions for GATE DA with answers and detailed solutions. Free sample questions below.

    Chapter Roadmap: Continuous Probability and Geometric Probability

    Your journey through this chapter
    1
    Continuous Random Variables and PDFs
    From counting discrete outcomes to measuring continuous ones.
    2
    The Continuous Uniform Distribution
    The simplest continuous model, where every interval of the same length is equally likely.
    3
    Geometric Probability
    When chance meets geometry: lengths, areas, and volumes.
    4
    Joint Distributions and Area Methods
    Solving multi-variable problems by calculating areas in the plane.
    End goal: visualize probability as area under a curve or as a ratio of geometric measures, and solve continuous probability questions effortlessly.

    The Shift to Continuous: From Counting to Measuring

    The fundamental shift

    • Discrete: Outcomes are countable. We use a Probability Mass Function (PMF). .
    • Continuous: Outcomes are measurements (time, length, area). We use a Probability Density Function (PDF). .

    The Probability Density Function (PDF)

    For a continuous random variable , the PDF satisfies:

    1. for all .
    2. The total area under the curve is 1: .

    How to find probabilities

    The probability that falls in an interval is the area under the PDF over that interval:

    Key intuition: In continuous probability, you do not calculate the probability of a point; you calculate the probability of a region by measuring its area.

    Continuous Probability and Geometric Probability: Solved Questions with Step-by-Step Explanations (1 Problems)

    Question 1 · Probability and Statistics NAT
    Let be a random variable uniformly distributed in the interval [1, 3] and be a
    random variable uniformly distributed in the interval [2, 4]. If X and Y are
    independent of each other, the probability P() is ______ (rounded off to
    three decimal places).

    More previous year questions (pyqs) in this unit

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    Continuous Probability and Geometric Probability Previous Year Questions (PYQs) for GATE DA: 1+ Solved Questions with Step-by-Step Solutions

    Solve 1+ Continuous Probability and Geometric Probability previous year questions for GATE DA with answers and detailed solutions. Free sample questions below

    A question from this chapter

    Question 1
    Let be a random variable uniformly distributed in the interval [1, 3] and be a
    random variable uniformly distributed in the interval [2, 4]. If X and Y are
    independent of each other, the probability P() is ______ (rounded off to
    three decimal places).
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