The expectation of a random variable is the average value or mean of all possible outcomes of the variable. It is calculated by multiplying each possible outcome by its probability and then summing up all the products.
The expectation of a random variable is a theoretical value that represents the average outcome, while the actual values are the specific outcomes that may vary from trial to trial.
Yes, the expectation of a random variable can be negative. This means that the average outcome is lower than the expected value.
The expectation of a discrete random variable is calculated by multiplying each possible outcome by its probability and then summing up all the products. Mathematically, it can be represented as E(X) = ΣxP(x), where X is the random variable and P(x) is the probability of the outcome x.
No, the expectation of a continuous random variable cannot be calculated using the same formula as a discrete random variable. For continuous random variables, the expectation is calculated by integrating the product of the variable and its probability density function over its entire range. Mathematically, it can be represented as E(X) = ∫xf(x)dx, where X is the random variable and f(x) is its probability density function.