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Math Help - independent random variables

  1. #1
    Super Member Anonymous1's Avatar
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    independent random variables

    Suppose that A, B, C, are independent random variables, each being uniformly distributed over (0,1).

    (a) What is the joint cumulative distribution function of A, B, C?
    (b) What is the probability that all the roots of the equation Ax^2 + BX + C = 0 are real?
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    Hello,

    Let x,y,z in \mathbb{R}

    The cdf of (A,B,C) is P(A\leq x,B\leq y,C\leq z)=P(\{A\leq x\}\cap \{B\leq y\} \cap \{C\leq z\})

    But since A,B,C are independent, the probability of the intersection is the product of the probabilities

    So the cdf is P(A\leq x)P(B\leq y)P(C\leq z)
    And since you certainly know the cdf of a uniform distribution, you'll be able to answer the question...


    You have to find P(B^2-4AC\geq 0)=\int_0^1\int_0^1 \int_{2\sqrt{ac}}^1 db ~da ~dc

    Try to understand that...
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