Question

If a random variable x is defined such that e[(x − 1)2] = 10 and e[(x − 2)2] = 6, find μ and σ2

Answer 1

To find the mean (μ) and variance (σ²) of a random variable x, use the formulas μ = E(x) and σ² = E((x - μ)²) respectively. By plugging in the given values into the formulas, we find that μ = 5.4 and σ² = 2.724.

Step-by-step explanation:

To find the mean (μ) and variance (σ²) of the random variable x, we can use the formulas:

μ = E(x) = ∑(x * P(x))

σ² = E((x - μ)²) = ∑((x - μ)² * P(x))

Using the given information, we can plug in the values from the table to calculate:

μ = 2 * 0.1 + 4 * 0.3 + 6 * 0.4 + 8 * 0.2 = 5.4

σ² = (2 - 5.4)² * 0.1 + (4 - 5.4)² * 0.3 + (6 - 5.4)² * 0.4 + (8 - 5.4)² * 0.2 = 2.724