Practice Partial Differential Equations (13.) - Probability Density Function (pdf)

Practice: Partial Differential Equations

Lesson 13.Probability Density Function (pdf)

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9 questions

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6 sample questions

Question 1.
Define a Probability Density Function (PDF).
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Think about how we express probabilities for continuous variables.
Question 2.
What is the definition of non-negativity in the context of PDFs?
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Consider the graphical representation of a PDF.
3Question 3.
What describes the likelihood of a continuous random variable taking on a particular value?
- Probability Mass Function
- Probability Density Function
- Cumulative Distribution Function
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Think about continuous random variables.
4Question 4.
The total area under a PDF curve equals what?
- True
- False
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Consider how probabilities relate to areas.
Question 5.
A continuous random variable X follows a PDF given by f(x) = 2x for 0 ≤ x ≤ 1. Calculate the expected value E[X] and the variance Var(X).
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Set up your integrals carefully and simplify appropriately.
Question 6.
Given a normal distribution with mean μ = 0 and variance σ² = 1, compute the probability that a value lies between -1 and 1 using the standard normal table.
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Consider how the area under the curve represents probabilities.

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