If X is a continuous random variable on [A, B], then we could build up a...

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If X is a continuous random variable on [A, B], then we could build up a data set by repeatedly running the random event associated to X. A data set is just a collection of numbers so we could calculate its mean (the average value). Remarkably, as we repeat the random event, this mean will converge on a single value, called the expected value of X, denoted E(X). This is called the Law of Large Numbers. It's the reason casinos make money! It turns out that given the probability density function f(x) of X, we have B E(X) = [ x f(x)dx Now consider a continuous random variable X which takes values on [0, /2] with probability density function f(x) = 3 sin (x) cos(x) Calculate the expected value of X. If X is a continuous random variable on [A, B], then we could build up a data set by repeatedly running the random event associated to X. A data set is just a collection of numbers so we could calculate its mean (the average value). Remarkably, as we repeat the random event, this mean will converge on a single value, called the expected value of X, denoted E(X). This is called the Law of Large Numbers. It's the reason casinos make money! It turns out that given the probability density function f(x) of X, we have B E(X) = [ x f(x)dx Now consider a continuous random variable X which takes values on [0, /2] with probability density function f(x) = 3 sin (x) cos(x) Calculate the expected value of X.