How to interpret the array outcomes obtained from a distribution
1. In the video in poision distribution with lamda = 10, how are interpreting the array output obtained. what does it covey.?
2. Also how are you saying range is between 3 to 16 for the same posion distribtion without lamda, seed of 365 and size of (5,5).?
1 answers ( 0 marked as helpful)
From Numpy Documentation:
numpy.random.poisson(lam=1.0, size=None)
>>Draw samples from a Poisson distribution.
So, numpy.random.poisson(lam=5, size=30) returns a sample from the Poisson's distribution.
But what is a Poisson's distribution for starters.
In 1837, a French nice guy named Siméon Denis Poisson was drinking some tee after lunch and suddenly had an Idea, we knew the Bernoulli distribution, and then we knew the Binomial distribution, but, is that it? are we done? I have to think of somethign new, something different, I'll maek a hypothesis that no one thought of. Let's assume something, anything. And then he looked at his right and you know he was a scientist so he found a book. He said, that's it, I'll examine the number of typos inside that book. He searched and searched and at the end, he found 5 typos at the 60,000 words. Well, let's consider each word-examinig process as a trial, that's a Bernoulli distribution, ooh Bernoulli, you were a good gue. Now, we can consider reading the whole book as a series of trials, which means that we can use the Binomial distribution to predict how likely will we get 4 typos, or 8 typos, or 100 typos, well, that's interesting, let's write down the Binomial distribution formula to see that.
𝑷(𝒀=𝒚) = 𝑪(𝒚,𝒏)×𝒑^𝒚×(𝟏−𝒑)^(𝒏−𝒚)
That's the Binomial distribution function, where n is the number of words of the book (60,000) word, p is the probability of having typos (5 typos/ 60,000 words) and y is the number fo typos we want to know how likely would it happen (4 typos, 8 typos, 100 typos, ... etc).
He grapped his pen and started filling the numbers.
1- C(y, n) = n!/(n-y)!y!, but n is tooo large (60,000) and y is tooo small (8, 9, 100), so we can say that n! almost equal to (n-y)!, let's get them out of our equation to make it cleaner, C(y, n) = 1/y!.
2- p^y, that's already clean already.
the third part is something likethat.
Then he came up with his great formula that perdicts the likelihood of unusual (rare) events.
𝑷(𝒀=𝒚)=λ^𝒚(𝒆^−λ)/y!
numpy.random.poisson(lam=1.0, size=None)
>>Draw samples from a Poisson distribution.
So, numpy.random.poisson(lam=5, size=30) returns a sample from the Poisson's distribution.
But what is a Poisson's distribution for starters.
In 1837, a French nice guy named Siméon Denis Poisson was drinking some tee after lunch and suddenly had an Idea, we knew the Bernoulli distribution, and then we knew the Binomial distribution, but, is that it? are we done? I have to think of somethign new, something different, I'll maek a hypothesis that no one thought of. Let's assume something, anything. And then he looked at his right and you know he was a scientist so he found a book. He said, that's it, I'll examine the number of typos inside that book. He searched and searched and at the end, he found 5 typos at the 60,000 words. Well, let's consider each word-examinig process as a trial, that's a Bernoulli distribution, ooh Bernoulli, you were a good gue. Now, we can consider reading the whole book as a series of trials, which means that we can use the Binomial distribution to predict how likely will we get 4 typos, or 8 typos, or 100 typos, well, that's interesting, let's write down the Binomial distribution formula to see that.
𝑷(𝒀=𝒚) = 𝑪(𝒚,𝒏)×𝒑^𝒚×(𝟏−𝒑)^(𝒏−𝒚)
That's the Binomial distribution function, where n is the number of words of the book (60,000) word, p is the probability of having typos (5 typos/ 60,000 words) and y is the number fo typos we want to know how likely would it happen (4 typos, 8 typos, 100 typos, ... etc).
He grapped his pen and started filling the numbers.
1- C(y, n) = n!/(n-y)!y!, but n is tooo large (60,000) and y is tooo small (8, 9, 100), so we can say that n! almost equal to (n-y)!, let's get them out of our equation to make it cleaner, C(y, n) = 1/y!.
2- p^y, that's already clean already.
the third part is something likethat.
Then he came up with his great formula that perdicts the likelihood of unusual (rare) events.
𝑷(𝒀=𝒚)=λ^𝒚(𝒆^−λ)/y!
