Understanding Poisson Distribution with Example || Lesson 55 || Probability & Statistics ||

Understanding Poisson Distribution with Example
In this class, We discuss Understanding Poisson Distribution with Example.
The reader should have prior knowledge of binomial distribution. Click Here.
We use the example discussed in the Binomial distribution data analysis to understand the Poisson distribution.
This class will give you an idea of when to apply Poisson distribution.
The last class example has the following data.
Posted a youtube video for 30 days.
We got 300 views, and 60 likes to the video.
They asked the question probability of getting 4 likes tomorrow.
We find the n and p values from the data and apply binomial distribution.
How do we identify n and p values?
We got 300 views in 30 days. so 300/30 = 10 views per day.
probability of likes = 60/300 = 0.2
The data shows 60 likes in 30 days, so 60 / 30 ie 2 likes per day.
rate = likes per day = 2
If someone said, I would get on an average 2 likes per day. We do not have n value and p-value.
In this type of situation, we apply the Poisson distribution.
In a most real-life situations, we have the rate value.
Example: If we ask a doctor how many heart patients you deal with daily?
He says, on average, I deal with 2 heart patients daily.
He will never count the number of patients who visit his hospital and other information.
Example 2: Count the number of bikes going in one minute on a highway?
On average, 10 bikes go in one minute.
n and p-value are not available here.
Someone gave the rate value and asked you the probability. We go with the Poisson distribution.
rate = lambda = 2 in our example.
Important to Understand:
rate = lambda
The rate value comes with n and p values.
λ = np
From our example n = 10 and p = 0.2
λ = np = 10 * 0.2 = 2
Given rate value means multiplication of n and p-value.
Given λ = 2 and P(X = 4)? we go with poisson distribution.
Probability mass function of poisson distribution = (e^-λ λ^x)/x!
P(X=4) = (e^-2 2^4)/4!
P(X=4) = 0.0902
From our previous class, when we applied binomial distribution to the same example, we got the probability value = 0.08808
Poisson distribution is an approximation to the binomial distribution.
In our next classes, we understand how we got the probability mass function of the Poisson distribution?

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