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Statistics help: Probability density functions watch

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    Hey!! So this is the question:

    5) Consider the probability density function below and find h:

    Name:  stats.jpg
Views: 72
Size:  149.9 KB

    So I tried multiplying (0.2 - 0.1x) by h, finding the integral by using the bounds of 0 and 2, or 3 and 5, and then equating the integral to 1, then rearranging to find h, but the answers were completely wrong.

    Any ideas????

    Much appreciated!
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    The total area under any pdf is 1.

    So

    area under the part where f(x) = 0.2-0.1x

    +

    area under the part where f(x)=h

    = 1

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    (Original post by JaketheSnake72)
    Hey!! So this is the question:

    5) Consider the probability density function below and find h:

    Name:  stats.jpg
Views: 72
Size:  149.9 KB

    So I tried multiplying (0.2 - 0.1x) by h, finding the integral by using the bounds of 0 and 2, or 3 and 5, and then equating the integral to 1, then rearranging to find h, but the answers were completely wrong.

    Any ideas????

    Much appreciated!
    You are getting much to complicated much too early! Start by drawing a graph of the probability distribution, then the answer should leap out of the page at you.
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    Thanks! These really helped, I was completely overcomplicating it.

    I'm confused on another part of the question too. How do you find F(2.5)? Would it just be zero, seeing as 2.5 lies outside both ranges, or would I need to add the integral of F(2) + 0, seeing as its cumulative??
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    (Original post by JaketheSnake72)
    Thanks! These really helped, I was completely overcomplicating it.

    I'm confused on another part of the question too. How do you find F(2.5)? Would it just be zero, seeing as 2.5 lies outside both ranges, or would I need to add the integral of F(2) + 0, seeing as its cumulative??
    The cumulative function is the integral of the density function:

    \displaystyle F(x) = \int_{-\infty}^{x}f(t) dt

    So in this case F(2.5) involves finding the area under the curve of the first "bump" of that function.
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    (Original post by Gregorius)
    The cumulative function is the integral of the density function:

    \displaystyle F(x) = \int_{-\infty}^{x}f(t) dt

    So in this case F(2.5) involves finding the area under the curve of the first "bump" of that function.
    Oh, ok! So you mean the area between 0 and 2? Gotcha!
 
 
 
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