Lab 2
pdf
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School
Northeastern University *
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Course
6200
Subject
Industrial Engineering
Date
Jan 9, 2024
Type
Pages
10
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In [44]:
n
=
100 #sample size
n_experiments
=
1000 # replicates
heads_count =
np
.
random
.
binomial
(
n
, 0.5
, n_experiments
)
heads
, event_count =
np
.
unique
(
heads_count
, return_counts
=
True
)
event_proba =
event_count
/
n_experiments
plt
.
bar
(
heads
, event_proba
, color
=
'blue'
)
plt
.
xlabel
(
f'Heads flips (out of {
n
} tosses)'
)
_ =
plt
.
ylabel
(
'Event probability'
)
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In [39]:
import
numpy as
np
import
matplotlib.pyplot as
plt
# Generate a random normal distribution
mu =
0
sigma =
1
sample_size =
100
data =
np
.
random
.
normal
(
mu
, sigma
, sample_size
)
# Generate a sampling distribution
n_samples =
1000
sample_means =
[]
for
i in
range
(
n_samples
):
sample =
np
.
random
.
choice
(
data
, size
=
sample_size
)
sample_means
.
append
(
np
.
mean
(
sample
))
# Plot the histogram of the sample means
plt
.
hist
(
sample_means
, bins
=
30
,
edgecolor
=
"red"
)
plt
.
show
()
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In [5]:
# Generate your random samples
# Generate your sampling distribution
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array([ 0.0058, -1.2987, -0.9235, -2.3325, 0.9518, -0.4459, 1.6942,
0.9853, -0.6772, 0.115 ])
-0.2001710211476492
# Plot the histogram of the sample means
In [6]:
# Generate a random discrete distribution
# Generate a sampling distribution
# Plot the histogram of the sample total
In [217…
x =
np
.
random
.
normal
(
size
=
10000
)
x_sample =
np
.
random
.
choice
(
x
, size
=
10
, replace
=
False
) # generate a random sample
x_sample
Out[217]:
In [216…
np
.
mean
(
x_sample
)
Out[216]:
In [54]:
# Write a function to calculate the means for samples drawn from a given distribution
# Begin of your
function
def
sample_mean_calculator
(
input_dist
, sample_size
, n_samples
):
# Continue to finish the function
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# End of the function
In [219…
sns
.
histplot
(
sample_mean_calculator
(
x
, 10
, 20
), color
=
'green'
) #distribution plot
_ =
plt
.
xlim
(
-
1.5
, 1.5
)
In [221…
sns
.
displot
(
sample_mean_calculator
(
x
, 10
, 1000
), color
=
'green'
, kde
=
True
) # distribution plot with more rep
_ =
plt
.
xlim
(
-
1.5
, 1.5
)
# What are your observations with a larger number of replicates?
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In [ ]:
sns
.
displot
(
sample_mean_calculator
(
x
, 100
, 1000
), color
=
'green'
, kde
=
True
) # distribution plot with larger _ =
plt
.
xlim
(
-
1.5
, 1.5
) # What are your observations vs larger number of replicates?
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In [ ]:
sns
.
displot
(
sample_mean_calculator
(
x
, 1000
, 1000
), color
=
'green'
, kde
=
True
)
_ =
plt
.
xlim
(
-
1.5
, 1.5
) # your comments with large sample size and large number of replicates
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In [7]:
# Generate your 500 single observations
In [8]:
# Display your histogram (b) of 500 sample means of size 2
In [9]:
# Display your histogram (b) of 500 sample means of size 10
In [10]:
# Display your histogram (b) of 500 sample means of size 30