How do you find the expected value of an independent variable?
The expected value of the sum of several random variables is equal to the sum of their expectations, e.g., E[X+Y] = E[X]+ E[Y] .
How do you find E XY?
To obtain E(XY), in each cell of the joint probability distribution table, we multiply each joint probability by its corresponding X and Y values: E(XY) = x1y1p(x1,y1) + x1y2p(x1,y2) + x2y1p(x2,y1) + x2y2p(x2,y2).
How do you find the expected value of an ex?
The expected value of X is usually written as E(X) or m. So the expected value is the sum of: [(each of the possible outcomes) × (the probability of the outcome occurring)].
How to calculate the expectation of$ XY$?
If X and Y are independent random variables, then E[XY] = E[X]E[Y]. Note that this holds for all random variables, not just continuous random variables. Also, as you probably know, the converse is not true: uncorrelated random variables need not be independent.
How to calculate the expected value of a random variable?
We could use the independence of the two random variables X 1 and X 2, in conjunction with the definition of expected value of Y as we know it. First, using the binomial formula, note that we can present the probability mass function of X 1 in tabular form as: And, we can present the probability mass function of X 2 in tabular form as well:
Which is the expectation of function of n independent random variables?
In the special case that we are looking for the expectation of the product of functions of n independent random variables, the following theorem will help us out. That is, the expectation of the product is the product of the expectations. For the sake of concreteness, let’s assume that the random variables are discrete.
How to calculate the mean and variance of Y?
We can calculate the mean and variance of Y in three different ways. By recognizing that Y is a binomial random variable with n = 5 and p = 1 2, we can use what know about the mean and variance of a binomial random variable, namely that the mean of Y is: