# 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

### 2 Answers

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- rotchmLv 72 months agoFavorite 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?

- az_lenderLv 72 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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