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Math Help - Probability Density Function

  1. #1
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    Probability Density Function

    I'm sorta confused by this question on a probability density function:

    Let f(x) = kx^2 if 0< x < 2 and 0 otherwise. Find k such that f(x) qualifies as a continuous probability density function for a random variable X. Then find c1 and c2 such that P(X< c1)= 0.1 and P(X< c2)= 0.9

    I guess we need to start by solving for k. To do that, we need to set the integral of f(x) from 0 to 2 equal to 1, right? Please correct me if I'm wrong. Anyways, what I'm really confused about is the second part. I just cant figure out how to go about finding 2 random values...

    Thanks in advance if anyone can help!
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    Quote Originally Posted by alakaboom1 View Post
    Let f(x) = kx^2 if 0< x < 2 and 0 otherwise. Find k such that f(x) qualifies as a continuous probability density function for a random variable X. Then find c1 and c2 such that P(X< c1)= 0.1 and P(X< c2)= 0.9
    Find \mathbf k such that k\int\limits_0^2 {x^2 dx}  = 1.
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  3. #3
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    Thank you, but I said I already had that . I mainly need help with the second part of the problem.
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  4. #4
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    Quote Originally Posted by alakaboom1 View Post
    I'm sorta confused by this question on a probability density function:

    Let f(x) = kx^2 if 0< x < 2 and 0 otherwise. Find k such that f(x) qualifies as a continuous probability density function for a random variable X. Then find c1 and c2 such that P(X< c1)= 0.1 and P(X< c2)= 0.9

    I guess we need to start by solving for k. To do that, we need to set the integral of f(x) from 0 to 2 equal to 1, right? Please correct me if I'm wrong. Anyways, what I'm really confused about is the second part. I just cant figure out how to go about finding 2 random values...

    Thanks in advance if anyone can help!
    Solve \displaystyle \int_{0}^{c_1} f(x) \, dx = 0.1 for c_1. Other one done in same way.
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  5. #5
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    Ah, thats it. Thanks a lot!
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