Practice Random Variables: Definition (6.1) - Random Variables (Discrete and Continuous)

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6 sample questions

Question 1.
What is a random variable?
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Think about how outcomes in experiments can be quantified.
Question 2.
Give an example of a discrete random variable.
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Consider things that can be counted.
3Question 3.
What are random variables used for?
- To predict outcomes
- To count items
- To measure time
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Think about where uncertainty is present.
4Question 4.
Is a temperature reading a discrete random variable?
- True
- False
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Consider how temperature can change gradually.
Question 5.
In a game, a player wins $0, $1, or $2 with probabilities 0.5, 0.3, and 0.2 respectively. Calculate the expected value of their winnings.
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Use the expectation formula with given probabilities.
Question 6.
A continuous random variable has a PDF given by f(x) = 3x² for 0 ≤ x ≤ 1. Find the expectation of this variable.
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Integrate the product of x and the PDF within the defined limits.

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