How do you find the expected value of log x?

E[log(x)]≈log(E[x])−V[x]2E[x]2. This approximation seems to work pretty well for their application. Modifying this slightly to fit the question at hand yields, by linearity of expectation, E[log(1+x)]≈log(1+E[x])−V[x]2(1+E[x])2.

What is expectation of expectation of X?

The expected value (or mean) of X, where X is a discrete random variable, is a weighted average of the possible values that X can take, each value being weighted according to the probability of that event occurring.

Is log x the same as X?

So log(3) and log10(3) are one and the same thing, the same way x and 1x are the same thing: they tell you the same thing, but one has superfluous information. As you can see, log(x) and ln(x) are not the same thing! They involve the same concept, and are both logarithms, but they are still different things.

What are the expectations of a function of random variables?

The expectation of Bernoulli random variable implies that since an indicator function of a random variable is a Bernoulli random variable, its expectation equals the probability. Formally, given a set A, an indicator function of a random variable X is defined as, 1A(X) = { 1 if X ∈ A 0 otherwise .

Is expectation the same as mean?

There’s no difference. They are two names for the same thing. They tend to be used in different contexts, though. You talk about the expected value of a random variable and the mean of a sample, population or probability distribution.

What is the relationship between ln x and e x?

ln (x) and e x are inverse functions The natural logarithm function is defined to do exactly the opposite, namely: Therefore these are inverse functions. Note the following: We saw above that the solution of e x = y is x = ln (y).

What is the difference between a X and E X?

There is no difference, the difference is just of values. In a^x, a is any constant, and when you put a = e, you get e^x, hence a^x is a general form, while e^x is a specified form of a^x.

What is Expectation Vs Reality?

Expectations vs Reality Expectations are those that we consider as possible and likely to occur. These are our beliefs, hopes and dreams for the future. The reality, on the other hand, is the state of things as they are.