Normal Distribution EXPLAINED with Examples
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Normal Distribution EXPLAINED with Examples
Learn how to solve any Normal Probability Distribution problem. This tutorial first explains the concept behind the normal distribution, then it discusses how to find probabilities for this distribution, and finally it ends with a complete example to help solidify the concept. The normal distribution is one of the most popular probability ...
1.3M viewsMar 18, 2021
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Prove the Poisson approximation of binomial probabilities.Claim: If X   Bin(n, p) with np = λ (or p = λ/n) and n is large, then P(X = i) can be approximated by the Poisson probability with rate λ.Hint: Use (1 - λ/n)^i, (1 - λ/n)^n-i, and (n - i 1)^n as n → ∞. The last assumption implies that we use the approximation for moderate i only.Which of the following arguments justifies the Poisson approximation? All limits are as n → ∞.(a) lim (np) = λ, by assumption(b) lim [(1 i/n)^(-
Prove the Poisson approximation of binomial probabilities.Claim: If X   Bin(n, p) with np = λ (or p = λ/n) and n is large, then P(X = i) can be approximated by the Poisson probability with rate λ.Hint: Use (1 - λ/n)^i, (1 - λ/n)^n-i, and (n - i 1)^n as n → ∞. The last assumption implies that we use the approximation for moderate i only.Which of the following arguments justifies the Poisson approximation? All limits are as n → ∞.(a) lim (np) = λ, by assumption(b) lim [(1 i/n)^(-
numerade.com
Jan 29, 2023