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The two sides of a fair coin are labelled as 0 and 1. The coin is tossed two times independently. Let M and N denote the labels corresponding to the outcomes of those tosses. For a random variable X, defined as X = min{M, N), the expected value E(X) (rounded off to two decimal places) is ________ .
    Correct answer is '0.25'. Can you explain this answer?
    Verified Answer
    The two sides of a fair coin are labelled as 0 and 1. The coin is toss...
    s = {( H, H), (H, T), (T, H), (T, T)}


    Now, X = Min {M, N}
    ∴ X = Min {H, H} = Min{(1, 1)} = 1 
    X = Min {H, T} = Min{1, 0} = 0 
    X = Min{T, H} = Min{0, 1} = 0 
    X = Min{T, T} = Min{0, 0} = 0
    ∴ 

    We know that, E(X) = 
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    The two sides of a fair coin are labelled as 0 and 1. The coin is toss...
    Understanding the Problem:
    The problem describes a fair coin that is tossed two times independently. Each toss can result in either a 0 or a 1. The labels corresponding to the outcomes of the two tosses are denoted as M and N. The random variable X is defined as the minimum of M and N.

    Calculating the Expected Value:
    To find the expected value E(X), we need to calculate the average value of X over all possible outcomes of the two coin tosses. We can do this by considering all possible outcomes and their probabilities.

    Outcomes:
    Since each coin toss can result in either a 0 or a 1, there are four possible outcomes for the two coin tosses:
    - Outcome 1: M = 0, N = 0
    - Outcome 2: M = 0, N = 1
    - Outcome 3: M = 1, N = 0
    - Outcome 4: M = 1, N = 1

    Calculating the Probability:
    Since the coin is fair, each outcome has an equal probability of 1/4. Therefore, the probability of each outcome is as follows:
    - P(Outcome 1) = 1/4
    - P(Outcome 2) = 1/4
    - P(Outcome 3) = 1/4
    - P(Outcome 4) = 1/4

    Calculating the Minimum:
    Now, let's calculate the minimum for each outcome:
    - Minimum of Outcome 1: min(0, 0) = 0
    - Minimum of Outcome 2: min(0, 1) = 0
    - Minimum of Outcome 3: min(1, 0) = 0
    - Minimum of Outcome 4: min(1, 1) = 1

    Calculating the Expected Value:
    To find the expected value E(X), we need to calculate the weighted average of the minimum values over all possible outcomes:
    E(X) = P(Outcome 1) * Minimum of Outcome 1 + P(Outcome 2) * Minimum of Outcome 2 + P(Outcome 3) * Minimum of Outcome 3 + P(Outcome 4) * Minimum of Outcome 4

    Substituting the values:
    E(X) = (1/4) * 0 + (1/4) * 0 + (1/4) * 0 + (1/4) * 1
    E(X) = 0 + 0 + 0 + 1/4
    E(X) = 1/4

    Therefore, the expected value E(X) is 0.25 when rounded off to two decimal places.
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    The two sides of a fair coin are labelled as 0 and 1. The coin is tossed two times independently. Let M and N denote the labels corresponding to the outcomes of those tosses. For a random variable X, defined as X = min{M, N), the expected value E(X) (rounded off to two decimal places) is ________ .Correct answer is '0.25'. Can you explain this answer?
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    The two sides of a fair coin are labelled as 0 and 1. The coin is tossed two times independently. Let M and N denote the labels corresponding to the outcomes of those tosses. For a random variable X, defined as X = min{M, N), the expected value E(X) (rounded off to two decimal places) is ________ .Correct answer is '0.25'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The two sides of a fair coin are labelled as 0 and 1. The coin is tossed two times independently. Let M and N denote the labels corresponding to the outcomes of those tosses. For a random variable X, defined as X = min{M, N), the expected value E(X) (rounded off to two decimal places) is ________ .Correct answer is '0.25'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The two sides of a fair coin are labelled as 0 and 1. The coin is tossed two times independently. Let M and N denote the labels corresponding to the outcomes of those tosses. For a random variable X, defined as X = min{M, N), the expected value E(X) (rounded off to two decimal places) is ________ .Correct answer is '0.25'. Can you explain this answer?.
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