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Xis a random variable with uniform probability density function in the interval [-2,10], For Y = 2X- 6, the conditional probability P(Y< 7 I X > 5) (rounded off to three decimal places) is ____ .
    Correct answer is '0.3'. Can you explain this answer?
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    Xis a random variable with uniform probability density function in the...
    x follows uniform distribution over [-2, 10]
    ∴ 
    Given: y = 2x - 6
    ⇒ 
    For y = 7



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    Xis a random variable with uniform probability density function in the...
    = 4 | X = 2) is:

    First, we need to find the value of Y when X = 2:

    Y = 2X - 6 = 2(2) - 6 = -2

    So, we want to find P(Y = 4 | X = 2), which is the probability that Y = 4 given that X = 2.

    Using the formula for conditional probability:

    P(Y = 4 | X = 2) = P(Y = 4 and X = 2) / P(X = 2)

    Since X has a uniform probability density function in the interval [-2,10], its probability density function is:

    fX(x) = 1 / 12, for -2 <= x=""><=>

    Therefore, the probability of X = 2 is:

    P(X = 2) = fX(2) * (10 - (-2)) = 1 / 12 * 12 = 1

    Now, we need to find the joint probability P(Y = 4 and X = 2). Since Y = 2X - 6, we can solve for X in terms of Y:

    X = (Y + 6) / 2

    So, when Y = 4, we have:

    X = (4 + 6) / 2 = 5

    Therefore, P(Y = 4 and X = 2) = P(X = 5) = fX(5) * (10 - (-2)) = 1 / 12 * 12 = 1

    Putting it all together:

    P(Y = 4 | X = 2) = P(Y = 4 and X = 2) / P(X = 2) = 1 / 1 = 1

    So, the probability that Y = 4 given that X = 2 is 1.
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    Community Answer
    Xis a random variable with uniform probability density function in the...
    X follows uniform distribution over [-2, 10]
    ∴ 
    Given: y = 2x - 6
    ⇒ 
    For y = 7




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    Xis a random variable with uniform probability density function in the interval [-2,10], For Y = 2X- 6, the conditional probability P(Y< 7 I X > 5) (rounded off to three decimal places) is ____ .Correct answer is '0.3'. Can you explain this answer?
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    Xis a random variable with uniform probability density function in the interval [-2,10], For Y = 2X- 6, the conditional probability P(Y< 7 I X > 5) (rounded off to three decimal places) is ____ .Correct answer is '0.3'. 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 Xis a random variable with uniform probability density function in the interval [-2,10], For Y = 2X- 6, the conditional probability P(Y< 7 I X > 5) (rounded off to three decimal places) is ____ .Correct answer is '0.3'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Xis a random variable with uniform probability density function in the interval [-2,10], For Y = 2X- 6, the conditional probability P(Y< 7 I X > 5) (rounded off to three decimal places) is ____ .Correct answer is '0.3'. Can you explain this answer?.
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