Discussion Overview
The discussion revolves around the computation of the expected value E(X^3) for a random variable X that follows a normal distribution with parameters μ and σ². The context includes the calculation of covariance between X and Y, where Y is defined as X^2. Participants explore various methods to derive E(X^3) and its implications for the covariance calculation.
Discussion Character
- Technical explanation
- Mathematical reasoning
- Debate/contested
Main Points Raised
- One participant expresses difficulty in calculating Cov(X,Y) due to uncertainty about E(X^3), leading to a rearrangement involving E(X) and E(X^2).
- Another participant suggests using moment generating functions or integration by parts to compute E(X^3).
- A participant points out a potential confusion regarding the distinction between standard normal and normal distributions, indicating that if X is standard normal, E(X^3) would be zero, thus making Cov(X,Y) also zero.
- The original poster clarifies that they meant normal distribution rather than standard normal and acknowledges their need to revisit moment generating functions for the solution.
Areas of Agreement / Disagreement
Participants exhibit disagreement regarding the nature of the distribution of X and its implications for E(X^3). There is no consensus on the correct approach to compute E(X^3) or the resulting covariance.
Contextual Notes
There are unresolved assumptions regarding the parameters of the distribution and the methods allowed for computation. The discussion reflects varying levels of familiarity with statistical concepts, particularly moment generating functions and integration techniques.
Who May Find This Useful
This discussion may be useful for individuals studying probability and statistics, particularly those interested in the properties of normal distributions and covariance calculations.