find the expected value of the above random variable.
find the expected value of the above random variable.
Answer
Explanation:
Step1: Identify the expected value formula
The expected value $E(X)$ is the sum of products of scores $x_i$ and probabilities $P(x_i)$. $$E(X) = \sum_{i=1}^{n} x_i \cdot P(x_i)$$
Step2: Multiply each score by its probability
Calculate the product for each row in the table. $$1 \cdot 0.26 = 0.26$$ $$4 \cdot 0.22 = 0.88$$ $$8 \cdot 0.14 = 1.12$$ $$9 \cdot 0.27 = 2.43$$ $$10 \cdot 0.11 = 1.10$$
Step3: Sum the calculated products
Add all the individual products to find the total expected value. $$E(X) = 0.26 + 0.88 + 1.12 + 2.43 + 1.10$$
Step4: Perform the final addition
Calculate the final sum. $$E(X) = 5.79$$
Answer:
5.79