Probability density function

[jonny]

I'm having trouble with the continuous distribution. I can verify that f(x) satisfies the requirements for the uniform random variable X and find probabilities but am unsure where to start with continuous.

Here's an example

f(x) = -0.08x + 0.4, 0 <= x <= 5

I noticed this line is downward sloping unlike the examples in the book which are straight lines. I also know that requirement #1 is satisfied because all values between 0 and 5 are positive.

I am stuck on how to figure out if it satisfies requirement #2 and how to find probabilities such as P(x >= 3). Any help is appreciated.

[Outlier]

Maybe I'm missing something, but:
this plots out to be a triangle. The area of a triangle is [1/2]*base*height which area must be scaled so it equals 1, the total probability. Then figure out the area for the region where (x >= 3) using the same formula for the triangle's area.
In this case the total area already equals 1 so no scaling is req'd.

[jonny]

Ah, thank you. I didn't see it as a triangle I suppose :o.