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2 cards from this section. Quick, good the night before a test.
What is the formula to find the mean value of a function using direct integration?
Remember the integral symbol and what it represents.
Define the probability density function (PDF).
Think about how probabilities are assigned across a range.
What does the integral of a function F(x) multiplied by its probability distribution represent?
Consider what you are calculating over the distribution.
True or False: Direct integration is commonly used in engineering applications.
Think about complexity of functions encountered in practice.
Calculate the mean value of a function defined by where x follows a uniform distribution between -1 and 1.
Break the integral into parts and remember to apply the bounds of the uniform distribution.
Find the mean of a function involving two variables, F(x, y) = xy, where x and y are independent random variables uniformly distributed over [0, 1].
Carefully apply the integration in two dimensions by solving the inner integral first.
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