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The binomial distribution states that Prob(v successes in n trials ) = Bn,p(v) = n! v!(n − v)! Pº (1 '(1 − p)"- Show that as n → ∞ and p→ 0 the Binomial distribution approaches the Poisson distribution. Hint take μ = np and remember that (2)! = n(n − 1)(n − 2)(n − 3). (n − v + 1) n! (n-v)!

The binomial distribution states that Prob(v successes in n trials ) = Bn,p(v) = n! v!(n − v)! Pº (1 '(1 − p)"- Show that as n → ∞ and p→ 0 the Binomial distribution approaches the Poisson distribution. Hint take μ = np and remember that (2)! = n(n − 1)(n − 2)(n − 3). (n − v + 1) n! (n-v)!

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The binomial distribution states that n! v!(n − v)!P³ (1 − p)n- Prob(v successes in n trials ) = Bn,p(v) Show that as n → ∞ and p → 0 the Binomial distribution approaches the Poisson distribution. Hint take μ = np and remember that (n²v)! = n(n − 1)(n − 2)(n − 3) · (n − v + 1) n!
Transcribed Image Text:The binomial distribution states that n! v!(n − v)!P³ (1 − p)n- Prob(v successes in n trials ) = Bn,p(v) Show that as n → ∞ and p → 0 the Binomial distribution approaches the Poisson distribution. Hint take μ = np and remember that (n²v)! = n(n − 1)(n − 2)(n − 3) · (n − v + 1) n!
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