Practice Expectation (mean) (14.6.1) - Joint Probability Distributions

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6 sample questions

Question 1.
What is the expectation E[X] for a discrete random variable X with outcomes 1, 2, and 3 having probabilities 0.2, 0.5, and 0.3 respectively?
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Multiply each outcome by its probability and sum the results.
Question 2.
In a simple game, you can roll a die. What is the expected value of the roll?
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Use the average of the outcomes of a fair die.
3Question 3.
What is the formula for expectation E[X] for discrete random variables?
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Think of how averages are calculated.
4Question 4.
True or False: The expectation of a continuous random variable is obtained by a summation.
- True
- False
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Remember the difference between discrete and continuous cases.
Question 5.
Suppose X and Y are two independent random variables each with a mean of 3. Calculate E[X + 2Y].
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Use the linearity of expectation property.
Question 6.
Given the joint pdf f(x,y) = 6xy in the region [0,1] find E[XY].
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Make sure to set up the correct double integral.

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