Final answer:
The expected value of the given probability distribution is calculated using the formula E(X) = μ = Σ xP(x). After performing the calculations, the expected value, or mean, of the random variable X is determined to be 205.
Step-by-step explanation:
To calculate the expected value of a random variable X, you would use the formula E(X) = μ = Σ xP(x). In this formula, Σ denotes the sum across all possible values, x represents each value of the random variable, and P(x) represents the probability of that value. Applying this formula to the given probability distribution:
- X = 100, P(X) = 0.10
- X = 150, P(X) = 0.20
- X = 200, P(X) = 0.30
- X = 250, P(X) = 0.30
- X = 300, P(X) = 0.10
The calculation for the expected value is as follows:
E(X) = (100 × 0.10) + (150 × 0.20) + (200 × 0.30) + (250 × 0.30) + (300 × .10)
E(X) = 10 + 30 + 60 + 75 + 30
E(X) = 205
Therefore, the expected value of the random variable X is 205.