Asked by Bryanna Booker on Sep 26, 2024
Verified
For a random variable X,E(X + 2)− 5 = E(X)− 3,where E refers to the expected value.
Expected Value
The expected value is a statistical concept representing the average of all possible outcomes of a random variable, weighted by their probabilities.
Random Variable
A variable that can take on numerical results as outcomes of a random event.
- Comprehend the computation and implications of expected value and variance in probability distributions.
Verified Answer
AS
Amandeep Singhabout 15 hours ago
Final Answer :
True
Explanation :
Using properties of expected value, we have:
E(X + 2) - 5 = E(X) + E(2) - 5 (linearity of expected value)
= E(X) + 2 - 5
= E(X) - 3
Therefore, the equation holds for any random variable X.
E(X + 2) - 5 = E(X) + E(2) - 5 (linearity of expected value)
= E(X) + 2 - 5
= E(X) - 3
Therefore, the equation holds for any random variable X.
Learning Objectives
- Comprehend the computation and implications of expected value and variance in probability distributions.