Practice Examples And Applications (6.4) - Random Variables (Discrete and Continuous)

Practice: Examples and Applications

Lesson 6.4Random Variables (Discrete and Continuous)

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9 questions

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6 sample questions

Question 1.
What value can a discrete random variable take?
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Think of counting outcomes.
Question 2.
What is the expected value of rolling a fair six-sided die?
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Add up all possible outcomes and divide by total outcomes.
3Question 3.
What is the PMF for a discrete random variable?
- A function assigning probabilities to outcomes
- A measure of dispersion
- An expected value calculation
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Think about how probabilities are distributed for outcomes.
4Question 4.
TRUE or FALSE: Continuous random variables can take any value within an interval.
- True
- False
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Refer to the nature of continuous data.
Question 5.
A factory produces light bulbs with a defect rate of 10%. Define a discrete random variable X representing the number of defective bulbs in a sample of 10. Calculate its expected value and variance.
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Use the binomial distribution.
Question 6.
A random variable X has a PDF defined as f(x) = 3x² for 0 ≤ x ≤ 1. Find the expectation and variance of X.
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Remember to compute both E(X) and E[X²] for variance!

5 more questions in this section. Enroll free to practise them all.