Practice Partial Differential Equations (6) - Random Variables (Discrete and Continuous)

Practice: Partial Differential Equations

Lesson 6Random Variables (Discrete and Continuous)

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10 questions

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6 sample questions

Question 1.
What is a random variable?
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Think about how outcomes get mapped.
Question 2.
Name two examples of discrete random variables.
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Consider countable outcomes.
3Question 3.
What does a discrete random variable represent?
- Countable outcomes
- Uncountable outcomes
- Only continuous values
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Think about how we categorize outcomes.
4Question 4.
True or False: A PMF can be used to model continuous random variables.
- True
- False
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Recall the definitions of PMF and PDF.
Question 5.
A factory produces light bulbs, with a 5% chance of each bulb being defective. If you randomly select 10 bulbs, model the number of defective bulbs as a binomial distribution. What is the expected number of defective bulbs?
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Consider the probability of defectiveness for each bulb.
Question 6.
A car's speed is modeled as a continuous random variable with PDF f(x) = kx for 0 ≤ x ≤ 2. Determine k and then find the CDF.
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Use integration to derive the total area under the PDF.

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