Practice Discrete Random Variables (8.2.1) - Cumulative Distribution Function (CDF)

Practice: Discrete Random Variables

Lesson 8.2.1Cumulative Distribution Function (CDF)

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6 sample questions

Question 1.
What does the CDF measure?
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Think about what CDF stands for.
Question 2.
If a die is rolled, what is the PMF for each number from 1 to 6?
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Since it's a fair die.
3Question 3.
What is the main purpose of the CDF?
- To find the average value
- To measure cumulative probabilities
- To determine variance
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Think about how it accumulates values.
4Question 4.
True or False: The CDF can sometimes decrease.
- True
- False
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Consider the property of accumulation.
Question 5.
Suppose we have a biased die with the following PMF: {1: 0.1, 2: 0.2, 3: 0.4, 4: 0.1, 5: 0.1, 6: 0.1}. Calculate F(4). What does this tell you about the probabilities related to outcomes less than or equal to 4?
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Sum the probabilities for outcomes 1 through 4.
Question 6.
In an engineering application, a component’s life expectancy follows the PMF {<1 year: 0.15, 1-2 years: 0.25, 2-3 years: 0.4, >3 years: 0.2}. Determine the CDF at the end of 2 years and discuss its significance.
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Consider all probabilities up to the 2 years range.

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