veneratifer
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- Joined
- Dec 29, 2022
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What is the limit (if any exists) of this formula? Is it 1/2?
λ→∞limk=λ∑∞k!λke−λYour summation doesn't make much sense.What is the limit (if any exists) of this formula? Is it 1/2?λ→∞limk=λ∑∞k!λke−λ
Thank you for reply !Your summation doesn't make much sense.
1) λ is a constant parameter, you can't take the limit.
2) For the lower bound of the summation, k normally start at 0. Can you explain why is it starting at λ?
Essentially you're looking for the probability of the random variable being greater than or equal to its mean i.e. λ. Typically, we simply write Pr(X≥λ∣λ=c) , where c is some positive real number.Thank you for reply !
Probably you are right - my summation have no sense, but I don't know how to write this formally correct. My idea is as follow:
there is a poisson distribution of some event, I want to calculate probability that event occurs ≥λ times, so I sum PMF from λ to ∞ (the reason why lower bound of the summation start at λ)
import seaborn as sns
from matplotlib import pyplot as plt
import numpy as np
import math
plt.close('all')
lambdas = [.5,1,5,20,100,500] #Change different values of lambda here
f, ax = plt.subplots(2,3, figsize = (12,5))
for i,rate in enumerate(lambdas):
plt.subplot(2,3,i+1)
data = np.random.poisson(rate, size=10000)
plt.hist(data, bins=50, linewidth=1,histtype = 'stepfilled')
plt.title('\u03BB = '+ str(rate))
plt.subplots_adjust(hspace=0.5)
plt.show()