Sum of independent normal random variables is normal
Dependencies:
- Normal distribution
- Independence of random variables (incomplete)
- Distribution of sum of random variables (incomplete)
Let
Also,
Proof
https://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables#Proof_using_convolutions
Let
Dependency for:
Info:
- Depth: 10
- Number of transitive dependencies: 30
Transitive dependencies:
- /analysis/topological-space
- /sets-and-relations/countable-set
- /analysis/exponential-grows-superpolynomially
- /analysis/integration-by-parts
- /sets-and-relations/de-morgan-laws
- /measure-theory/linearity-of-lebesgue-integral
- /measure-theory/lebesgue-integral
- σ-algebra
- Generated σ-algebra
- Borel algebra
- Measurable function
- Generators of the real Borel algebra (incomplete)
- Measure
- σ-algebra is closed under countable intersections
- Group
- Ring
- Field
- Vector Space
- Probability
- Conditional probability (incomplete)
- Independence of events
- Independence of composite events
- Random variable
- Expected value of a random variable
- Distribution of sum of random variables (incomplete)
- Independence of random variables (incomplete)
- Linearity of expectation
- Variance of a random variable
- Gaussian integral (incomplete)
- Normal distribution