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3 cards from this section. Quick, good the night before a test.
What is the expectation of rolling a fair 6-sided die?
Use the average of the outcomes from 1 to 6.
If a coin is flipped, what is the expected number of heads in 3 flips?
Consider the probability of heads in each flip.
What is the expected value of a fair 6-sided die?
Think about the sum of the possible results divided by the number of outcomes.
True or False: The expectation of the sum of random variables equals the sum of their expectations.
Consider how averages aggregate.
Given a PDF f(x) = 2x for 0 < x < 1, calculate E(X).
Use integration to find the average under the probability density function.
Explain how stochastic PDEs arise in real-world scenarios. Provide a detailed example.
Connect physical systems and randomness in your explanation.
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