Find the value of q such that P(X<q)=1/4. Give your answer as a decimal correct to 3 decimal places.?

The continuous random variable X has a probability density function (pdf) given by

f(x)={1−x/2 for 0≤x≤2

         0 otherwise 

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  • rotchm
    Lv 7
    2 months ago
    Favorite Answer

    You are requested to find q such that

    q

    ∫ 1-x/2  dx  = 1/4.

    0

    So, integrate, evaluate & solve for q.

    Or, via highschool geometry:

    sketch 1-x/2. Its a triangle. Find q such that the area to the left is 1/4. 

    So, whats your final asnwer?

  • 2 months ago

    So the PDF is 1 at x=0 and 0 at x = 2,  think of the triangle whose upper boundary is 1 - x/2.

    You want an x value such that the triangle to the RIGHT of that x-value has an area of 3/4.

    (2 - x)*(1 - x/2)*(1/2) = 3/4 =>

    (2 - x)*(2 - x) = 3 =>

    (2 - x)^2 = 3 =>

    x = 2 - sqrt(3) = 0.268

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