How Do You Calculate Probability Using a Density Function?

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SUMMARY

The discussion focuses on calculating probabilities using a specific probability density function (PDF) defined for a continuous random variable X. The PDF is defined as f(x) = x for 0 < x < 1 and f(x) = 2 - x for 1 ≤ x < 2, with f(x) = 0 elsewhere. It is established that P(0 < X < 2) equals 1, confirming that the total probability integrates to 1 over the defined range. Additionally, the probability P(X < 1.2) can be computed by integrating the PDF over the appropriate intervals.

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  • Understanding of continuous random variables
  • Knowledge of probability density functions (PDFs)
  • Familiarity with integration techniques
  • Basic concepts of probability theory
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  • Learn how to compute probabilities using integration of PDFs
  • Study the properties of continuous random variables
  • Explore the concept of cumulative distribution functions (CDFs)
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mrvirgo
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A continuous random variable X has the density function
f(x)=x for 0<x<1
2-x for 1 _<x<2
0 elsewhere.
a. Show that P(0<X<2)=1
B. Find P(X<1.2).


Please see the attached file.
Thank
 

Attachments

Physics news on Phys.org
1. A lot of people will not open files for fear of viruses.

2. Here, there was no point in attaching the file since it doesn't say anything you haven't written here! In particular, there is not attempt at the problem youself.
How is P(a< X< b) defined for any probability density function f(x)? Where exactly is your difficulty?
 

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