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Given a random variable with probability density function f(x), how to compute the expected value of this random variable in R?
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To find the expected value, E(X), or mean μ of a discrete random variable X, simply multiply each value of the random variable by its probability and add the products. The formula is given as E(X)=μ=∑xP(x).
For any random variable X , the variance of X is the expected value of the squared difference between X and its expected value: Var[X] = E[(X-E[X])2] = E[X2] - (E[X])2 .
If you want to compute the expected value, just compute :
E(X) = Integral of xf(x)dx over the whole domain of X.
The integration can easily be done using the function integrate().
Say you're having a normal density function (you can easily define your own density function) :
f <- function(x){
1/sqrt(2*pi)*exp((-1/2)*x^2)
}
You calculate the expected value simply by:
f2 <- function(x){x*f(x)}
integrate(f2,-Inf,Inf )
Pay attention, sometimes you need to use Vectorize() for your function. This is necessary to get integrate to work. For more info, see the help pages of integrate() and Vectorize().
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Does it help to know that the expectation E is the integral of x*f(x) dx for x in (-inf, inf)?
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