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ET IN ARCADIA EGO

ET IN ARCADIA EGO
derblaue52
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derblaue52
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6 Comments

rayjdearn

Posted

On 6/18/2021 at 11:46 PM, duck said:

renneschateau05_002-768x546.thumb.jpg.ffe21fe4740646705079854b1a435413.jpg

ET IN ARCADIA EGO, BY NICOLAS POUSSIN

Sorry, I'm gay. I don't like Poussin.

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duck

Posted

Well there is a non-sequitur if there ever was one🤡.

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jakester

Posted

On 8/1/2021 at 7:40 AM, duck said:

Well there is a non-sequitur if there ever was one🤡.

Fish. (Poisson, I know, but clearly someone went to college.)

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jakester

Posted

On 6/19/2021 at 2:46 AM, duck said:

renneschateau05_002-768x546.thumb.jpg.ffe21fe4740646705079854b1a435413.jpg

ET IN ARCADIA EGO, BY NICOLAS POUSSIN

It's about death, not hardons. Death is the ego.

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duck

Posted

19 minutes ago, jakester said:

Fish. (Poisson, I know, but clearly someone went to college.)

Poisson Distribution Table

As with the binomial distribution, there is a table that we can use under certain conditions that will make calculating probabilities a little easier when using the Poisson Distribution. The table is showing the values of f(x) = P(X ≥ x), where X has a Poisson distribution with parameter λ. Refer the values from the table and substitute it in the Poisson distribution formula to get the probability value. The table displays the values of the Poisson distribution.

Poisson Distribution Table

Poisson Distribution Mean and Variance

Assume that, we conduct a Poisson experiment, in which the average number of successes within a given range is taken as λ. In Poisson distribution, the mean of the distribution is represented by λ and e is constant, which is approximately equal to 2.71828. Then, the Poisson probability is:

P(x, λ ) =(e– λ λx)/x!

In Poisson distribution, the mean is represented as E(X) = λ.

For a Poisson Distribution, the mean and the variance are equal. It means that E(X) = V(X)

Where,

V(X) is the variance.

Poisson Distribution Expected Value

A random variable is said to have a Poisson distribution with the parameter λ, where “λ” is considered as an expected value of the Poisson distribution.

The expected value of the Poisson distribution is given as follows:

E(x) = μ = d(eλ(t-1))/dt, at t=1.

E(x) = λ

Therefore, the expected value (mean) and the variance of the Poisson distribution is equal to λ.

Poisson Distribution Examples

An example to find the probability using the Poisson distribution is given below:

Example 1:

A random variable X has a Poisson distribution with parameter λ such that P (X = 1) = (0.2) P (X = 2). Find P (X = 0).

Solution:

For the Poisson distribution, the probability function is defined as:

P (X =x) = (e– λ λx)/x!, where λ is a parameter.

Given that, P (x = 1) = (0.2) P (X = 2)

(e– λ λ1)/1! = (0.2)(e– λ λ2)/2!

⇒λ = λ2/ 10

⇒λ = 10

Now, substitute λ = 10, in the formula, we get:

P (X =0 ) = (e– λ λ0)/0!

P (X =0) = e-10 = 0.0000454

Thus, P (X= 0) = 0.0000454

Example 2:

Telephone calls arrive at an exchange according to the Poisson process at a rate λ= 2/min. Calculate the probability that exactly two calls will be received during each of the first 5 minutes of the hour.

Solution:

Assume that “N” be the number of calls received during a 1 minute period.

Therefore,

P(N= 2) = (e-2. 22)/2!

P(N=2) = 2e-2.

Now, “M” be the number of minutes among 5 minutes considered, during which exactly 2 calls will be received. Thus “M” follows a binomial distribution with parameters n=5 and p= 2e-2.

P(M=5) = 32 x e-10

P(M =5) = 0.00145, where “e” is a constant, which is approximately equal to 2.718. 

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