SUMMARY
When X follows a normal distribution X ~ N(2,4), the transformation Y = -X - 1 results in Y also being a normal random variable, specifically Y ~ N(μ,σ^2). The expected value of Y is calculated as E(Y) = -E(X) - 1, yielding μ = -3. The variance of Y remains unchanged from that of X, thus σ^2 = 4.
PREREQUISITES
- Understanding of normal distributions and their properties
- Knowledge of expected value and variance calculations
- Familiarity with random variable transformations
- Basic statistics concepts
NEXT STEPS
- Study the properties of normal distributions in detail
- Learn about transformations of random variables
- Explore the implications of linear transformations on variance
- Review examples of calculating expected values and variances for different distributions
USEFUL FOR
Statisticians, data analysts, and students studying probability and statistics who need to understand transformations of random variables and their implications on expected values and variances.