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Understanding Continuous Random Variables and Probability Density Functions

This text delves into continuous random variables (CRVs) and their probability density functions (PDFs). It explains that the total area under a PDF equals 1, highlighting how probabilities can be computed by finding areas under the curve for specific value ranges. Examples include calculating probabilities for a given random variable and examining a bakery's production process to determine rejection rates of pastry sheets based on thickness. This foundational knowledge aids in further understanding distributions and their applications.

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Understanding Continuous Random Variables and Probability Density Functions

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  1. Continuous Random Variables Probability Density Functions (PDF)

  2. From yesterday Hopefully you noticed:

  3. Also if X and Y are independent random variables

  4. Probabilities of a CRV The total area under a probability density function is equal to 1 Particular probabilities are found by finding the areas under the curve between the required values.

  5. Example A random variable has the pdf: Draw the pdf Find P(X<12) Find P(X>22.5) Find P(6.3<X<11.8)

  6. Example A bakery producing pastry sheets believes that the thickness of the sheets is uniformly distributed between 1.5mm and 2.0mm. Pastry sheets with a thickness below 1.6mm are rejected. What percentage of the sheets are rejected?

  7. Page 128 – 139 can now all be done… Tomorrow we will look at the triangle distribution then have Friday in class to work on problems to try catch up. If you need more questions than your homework book I will have some others…

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