(Python3) Use the provided cells as a reference to write a for loop that plots the Poisson PDF for a range of λ values from 10 to 100 (by tens) on a single plot. lam = 75# return the n value corresponding to the 0.1 percentilemink = stats.poisson.ppf(0.001, lam)# return the n value corresponding to the 99.9 percentilemaxk = stats.poisson.ppf(0.999, lam)print (mink, maxk)50.0 103.0[90] create a range of x values over which to compute the PDF, ranging from minn to maxnx = np.arange(mink,maxk)len(x)53Now we're ready to actually compute the PDF, though actually in this case because the poisson distribution is discrete, this is more properlycalled a PMF (Probability Mass Function):[91] # compute pmf for given lam and range of xpoisson_pmf = stats.poisson.pmf(x, lam)We can also just as easily compute the cumulative distribution function:[92] poisson_cdf = stats.poisson.cdf(x, lam) should follow a Poisson distribution. The probability density function is given by:akP(k) = e¯^¸k!where is the mean of the distribution, so in a way, the expected number of occurrences, and k is the observed number of "occurrences" (anatural number, i.e. integers starting at 0) in some time t. We will need to define a range of values for k over which to calculate the pdf, and itcan be difficult to choose these intelligently. One trick is to use the "percent point function" to evaluate the k value corresponding to a certainpercentile of the full distribution. For example ppf(0.01) corresponds to the k value where only 1% of the area under the PDF is less than k.Let's create an appropriate range of k values for an arbitrary choice of 1:

Answered: (Python3) Use the provided cells as a…

Computer Networking: A Top-Down Approach (7th Edition)

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Question

(Python3) Use the provided cells as a reference to write a for loop that plots the Poisson PDF for a range of λ values from 10 to 100 (by tens) on a single plot.

lam = 75
# return the n value corresponding to the 0.1 percentile
mink = stats.poisson.ppf(0.001, lam)
# return the n value corresponding to the 99.9 percentile
maxk = stats.poisson.ppf(0.999, lam)
print (mink, maxk)
50.0 103.0
[90] create a range of x values over which to compute the PDF, ranging from minn to maxn
x = np.arange(mink,maxk)
len(x)
53
Now we're ready to actually compute the PDF, though actually in this case because the poisson distribution is discrete, this is more properly
called a PMF (Probability Mass Function):
[91] # compute pmf for given lam and range of x
poisson_pmf = stats.poisson.pmf(x, lam)
We can also just as easily compute the cumulative distribution function:
[92] poisson_cdf = stats.poisson.cdf(x, lam)

should follow a Poisson distribution. The probability density function is given by:
ak
P(k) = e¯^¸
k!
where is the mean of the distribution, so in a way, the expected number of occurrences, and k is the observed number of "occurrences" (a
natural number, i.e. integers starting at 0) in some time t. We will need to define a range of values for k over which to calculate the pdf, and it
can be difficult to choose these intelligently. One trick is to use the "percent point function" to evaluate the k value corresponding to a certain
percentile of the full distribution. For example ppf(0.01) corresponds to the k value where only 1% of the area under the PDF is less than k.
Let's create an appropriate range of k values for an arbitrary choice of 1:

Expert Solution

Step 1

A Poisson distribution is a distribution which shows the likely number of times that an event will occur within a pre-determined period of time. It is used for independent events which occur at a constant rate within a given interval of time.

matplotlib.pyplot is a collection of functions that make matplotlib work like MATLAB. Each pyplot function makes some change to a figure: e.g., creates a figure, creates a plotting area in a figure, plots some lines in a plotting area, decorates the plot with labels, etc.