If X and Y are each normal and uncorrelated then they are independent
Is this true?
No — it is false.
Others that fail the same way
- Convergence in probability ⇒ almost sure convergence
- Uncorrelated ⇒ independent
- Pairwise independent events are mutually independent
- Every random variable has a moment generating function
- A mixture of two distributions is a linear combination of the variables
- The maximum of independent exponentials is exponential
From Probability › Joint distributions, transformations, order statistics