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- How do you find the expected value of a random variable product?
- What is the expectation of the product of two random variables?
- What is the expected value for a random variable?
- How do you find the expected value of two random variables?
How do you find the expected value of a random variable product?
Properties of independent random variables: If X and Y are independent, then: – The expectation of the product of X and Y is the product of the individual expectations: E(XY ) = E(X)E(Y ). More generally, this product formula holds for any expectation of a function X times a function of Y .
What is the expectation of the product of two random variables?
In general, the expected value of the product of two random variables need not be equal to the product of their expectations. However, this holds when the random variables are independent: Theorem 5 For any two independent random variables, X1 and X2, E[X1 · X2] = E[X1] · E[X2].
What is the expected value for a random variable?
The expected value of a random variable is denoted by E[X]. The expected value can be thought of as the “average” value attained by the random variable; in fact, the expected value of a random variable is also called its mean, in which case we use the notation µX.
How do you find the expected value of two random variables?
For any two random variables X and Y , E(X+Y)=E(X)+E(Y) E ( X + Y ) = E ( X ) + E ( Y ) That is, the expected value of the sum is the sum of expected values, regardless of how the random variables are related.
