Practice Continuous Random Variables (6.3) - Random Variables (Discrete and Continuous)

Practice: Continuous Random Variables

Lesson 6.3Random Variables (Discrete and Continuous)

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10 questions

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6 sample questions

Question 1.
What is a continuous random variable?
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Think of examples like temperature or time.
Question 2.
Which function represents the probability of a continuous RV?
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Remember, it's a curve that describes probabilities.
3Question 3.
What is the primary purpose of a probability density function?
- To provide a list of probabilities
- To describe densities over intervals
- To show discrete outcomes
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Think about what a PDF represents graphically.
4Question 4.
The cumulative distribution function ranges from:
- -∞ to +∞
- 0 to 1
- 0 to ∞
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Consider how probabilities are represented in total.
Question 5.
Given the PDF f(x) = 6x(1-x) for 0 ≤ x ≤ 1, calculate the expectation value E(X) and the variance Var(X).
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First find the integral for E(X), then use the result to find Var(X).
Question 6.
If a continuous random variable has a CDF F(x) = x^3 for 0 ≤ x ≤ 1, find the PDF and verify it integrates to 1.
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Differentiate the CDF to find the PDF, then integrate.

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