Practice Expectation For Continuous Random Variables (9.1.3) - Expectation (Mean)

Practice: Expectation for Continuous Random Variables

Lesson 9.1.3Expectation (Mean)

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9 questions

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6 sample questions

Question 1.
What is the expectation of a random variable X uniformly distributed between 0 and 10?
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Use the formula for uniform distribution.
Question 2.
How does expectation relate to the average value?
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Consider the definition of mean.
3Question 3.
What is the expectation E(X) for a continuous variable with pdf f(x)?
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Think about the integral definition related to area under a curve.
4Question 4.
True or False: The expectation of a random variable is always a value that the variable can take.
- True
- False
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Consider how averages can sometimes lie outside the original set, like for a uniform distribution.
Question 5.
Consider a continuous random variable X with pdf f(x) = 2x for 0 <= x <= 1. Calculate the expectation E(X) and interpret the result.
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Set up the integral carefully and bear in mind the function shape.
Question 6.
A stock's price follows a normal distribution with a mean of $50 and standard deviation of $10. Calculate the expected price after 1 year assuming the same conditions hold.
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Consider why the mean value remains constant.

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