The first property of expected values listed here comes from the definition of linearity of expectation. It states that the expected value of the sum of random variables is equal to the sum of the expectation of each individual random variable. A simple example would be finding the expected value of rolling two six-sided dice. In this case, it would be the expectation of the first die + the expectation of the second die. 3.5 + 3.5 = 7
ksaralle
for me it was a leap to go from line 2 to line 3. i think for those of us unfamiliar with statistics it's important to remember that E[f(X)] = integral of f(x)p(x)dx and this transformation is nothing to overthink about because we are just substituting that equation in here.
The first property of expected values listed here comes from the definition of linearity of expectation. It states that the expected value of the sum of random variables is equal to the sum of the expectation of each individual random variable. A simple example would be finding the expected value of rolling two six-sided dice. In this case, it would be the expectation of the first die + the expectation of the second die. 3.5 + 3.5 = 7
for me it was a leap to go from line 2 to line 3. i think for those of us unfamiliar with statistics it's important to remember that E[f(X)] = integral of f(x)p(x)dx and this transformation is nothing to overthink about because we are just substituting that equation in here.