Practice Cdf For Discrete And Continuous Random Variables (8.2)

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9 questions

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6 sample questions

Question 1.
Define what a CDF is.
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Think about what the function describes.
Question 2.
What is the range of values for a CDF?
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What are the limits of probabilities?
3Question 3.
What does the CDF for a discrete random variable represent?
- P(X < x)
- P(X ≤ x)
- P(X > x)
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Remember what the CDF is defined as.
4Question 4.
True or False: The CDF can decrease as x increases.
- True
- False
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Think about the probability structure.
Question 5.
Prove that the CDF of a discrete random variable must approach 1 as x approaches infinity.
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Consider how cumulative probabilities work with respect to the definition of total probability.
Question 6.
For a continuous random variable defined by f(x) = 4x^(3) on [0,1], find the CDF at x = 0.75 and discuss the behavior near 1.
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Set up your integral for the PDF correctly, and consider limits at the endpoint.

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