Answer :
Final answer:
The expected value E(X) for the given probability distribution is calculated by multiplying each value of X by its probability, then adding up the products. In this case, E(X) = 26.5.
Explanation:
To calculate the expected value of X, E(X), for the given probability distribution, we use the formula E(X) = μ = Σ xP(x), where μ is the mean, x is each value of the random variable, and P(x) is the probability of x occurring. The expected value represents the long-term average if the experiment is repeated many times. Here is the calculation step by step:
- Multiply each value of X by its probability: (10 * 15/20) + (20 * 20/50) + (30 * 5/50) + (40 * 10/50).
- Simplify and calculate each product: (10 * 0.75) + (20 * 0.40) + (30 * 0.10) + (40 * 0.20).
- Add up all the products: 7.5 + 8 + 3 + 8.
- Calculate the sum to find E(X): 7.5 + 8 + 3 + 8 = 26.5
Therefore, the expected value of X, E(X), is 26.5.
