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Math Help - Continuous probability - conditional probability

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    Continuous probability - conditional probability

    Suppose that Y has density function

    f(y)=\left\{\begin{array}{cc}ky(1-y),&0\leq y\leq 1\\0, & \mbox{elsewhere}\end{array}\right.

    a. Find the value of kthat makes f(y) a probabilty density function.
    No problem, found k=6
    b. Find P(.4 \leq Y \leq 1) = \int^{1}_{.4}6y(1-y)dy=.648

    the part I am having trouble with is;
    d. Find P(Y \leq .4 | Y \leq .8)
    not too sure if P(Y \leq .4 | Y \leq .8)=\frac{P(.4 \leq Y \leq .8)}{P(Y \leq .8)} or how to calculate this conditional probability...
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  2. #2
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    Quote Originally Posted by Robb View Post
    Suppose that Y has density function

    f(y)=\left\{\begin{array}{cc}ky(1-y),&0\leq y\leq 1\\0, & \mbox{elsewhere}\end{array}\right.

    a. Find the value of kthat makes f(y) a probabilty density function.
    No problem, found k=6
    b. Find P(.4 \leq Y \leq 1) = \int^{1}_{.4}6y(1-y)dy=.648

    the part I am having trouble with is;
    d. Find P(Y \leq .4 | Y \leq .8)
    not too sure if P(Y \leq .4 | Y \leq .8)=\frac{P(.4 \leq Y \leq .8)}{P(Y \leq .8)} Mr F says: This should be {\color{red}P(Y \leq .4 | Y \leq .8)=\frac{P(Y \leq .4 \, \text{ and } \, Y \leq .8)}{P(Y \leq .8)}}.

    or how to calculate this conditional probability...
    Note that P(Y \leq .4 \, \text{ and } \, Y \leq .8) = P(Y \leq .4).

    Therefore P(Y \leq .4 \, | \, Y \leq .8) = \frac{P(Y \leq .4)}{P(Y \leq .8)} and you should be able to calculate those two things.
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