In this video I go over an example on determining whether a function is a Probability Density Function (PDF) as well as determine the probability that the random variable lies within a given range. As explained in my last video, the probability density function is modeled from real world experimental data so to ensure that the function given is actually a PDF, we need to ensure it meets the following two conditions:
- The function is always positive.
- The area under the function is equal to 1.
This is a useful video for understanding PDFs and proving if a given function is one. I also go over some very interesting algebra techniques in solving the example without needing to use a calculator, so make sure to watch this video!
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Applications of Integrals: Probability: Example 1
Let f(x) = 0.006x(10 - x) for 0 ≤ x ≤ 10 and f(x) = 0 for all other values of x.
a) Verify that f is a probability density function
b) Find P(4 ≤ X ≤ 8).
Solution:
