Introduction to Probability · free preview
Cumulative Distribution Functions and Functions of Random Variables
The CDF as the universal profile of any random variable, its properties, and how a function of a random variable acquires its own distribution.
1. The CDF and why it outranks the PMF
The CDF and why it outranks the PMF
2. Reading the staircase
Reading the staircase
3. Functions of a random variable
Functions of a random variable
4. CDF properties
Which of these functions cannot be a CDF?
5. Interval probability from the CDF
A CDF has F(2) = 0.45 and F(5) = 0.85. What is P(2 < X is at most 5)?
6. Decoding a jump
A discrete CDF has F(3) = 0.55 and left limit F(3^-) = 0.25. What is P(X = 3)? Enter a decimal like 0.3.
7. Two-to-one transform
X is a fair die roll and Y is 1 when X is at least 5 and 0 otherwise. What is P(Y = 1)? Enter a fraction like 1/3.
8. Squaring injectively
X takes values minus 2, minus 1, 0, 1, 2 each with probability 1/5. Let Y = X squared. What is P(Y = 4)? Enter a decimal like 0.4.
9. In your own words
In your own words, state the most important definition, theorem or method of this lesson and explain what it says.
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