Practice Continuous Random Variables (8.2.2) - Cumulative Distribution Function (CDF)

Practice: Continuous Random Variables

Lesson 8.2.2Cumulative Distribution Function (CDF)

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8 questions

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4 cards from this section. Quick, good the night before a test.
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Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Define CDF and how it is used for continuous random variables.
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Think of how you define probabilities.
Question 2.
What does it mean for a function to be non-decreasing?
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Consider how this looks on a graph.
3Question 3.
What is the main purpose of a CDF?
- To describe the probability of a variable being greater than a value
- To calculate the mean of a random variable
- To describe the probability of a variable being less than or equal to a value
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Think about what the CDF computes.
4Question 4.
Is the CDF for continuous variables a jump function?
- True
- False
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Consider the properties of continuous functions.
Question 5.
Given a continuous random variable with the PDF defined as f(x) = 6x(1-x) for x in [0,1], derive the CDF F(x).
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Use integration by parts or the power rule.
Question 6.
Consider a random variable X with the CDF defined as F(x) = x^3 for x in [0,1]. What is its PDF?
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Recall the relationship between CDF and PDF.

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