Question
In: Statistics and Probability
The daily rainfall in Cork (measured in millimeters) is modelled using a gamma distribution with parameters...
The daily rainfall in Cork (measured in millimeters) is modelled using a gamma distribution with parameters α = 0.8 and β = 0.3.
1) Use Markov’s inequality to upper bound the probability that the observed rainfall in a given day is larger than 3 mm, and compare the value to the result of cdf calculation.
2) Consider the overall rainfall in 365 days, and use moment generating functions and their properties to prove that this is Ga (292, 0.3).
3) Use the central limit theorem to approximate the probability that the annual rainfall exceeds 800mm (write down the analytical formula and the code used to calculate the cdf value).
Solutions
orchestra answered 2 years agoRelated Solutions
The daily rainfall in Japan (measured in millimeters) is modelled using a gamma distribution with parameters...
The daily rainfall in Japan (measured in millimeters) is
modelled using a gamma distribution with parameters α = 0.8 and β =
0.4.
Consider the overall rainfall in 365 days, and use mgfs and
their properties to prove that this is Ga (292, 0.4).
Use the central limit theorem to approximate the probability
that the annual rainfall exceeds 800mm (write down the analytical
formula and the code used to calculate the cdf value).
Compare the approximate value obtained with the...
1. The daily rainfall in Dublin (measured in millimeters) is modelled using a gamma distribution with...
1. The daily rainfall in Dublin (measured in millimeters) is
modelled using a gamma distribution with parameters α = 0.8 and β =
0.4.
(d) Use the central limit theorem to approximate the probability
that the annual rainfall exceeds 800mm (write down the analytical
formula and the code used to calculate the cdf value).
(e) Compare the approximate value obtained with the exact
counterpart (include the R code used to calculate the cdf
value).
(f) Use R to produce a...
Suppose that Y has the gamma distribution with parameters a ( shape ) = 2 and...
Suppose that Y has the gamma distribution with parameters a (
shape ) = 2 and b (scale) = 2. Use R to plot the probability
density, and determine the shape or skewness for the gamma
distribution.
Use R code
a. )Skew to the left
b.)
Skew to the right
c.)
symmetrical
d.)
bell curved
The frequency distribution below shows the distribution of average seasonal rainfall in San Francisco, as measured...
The frequency distribution below shows the distribution of
average seasonal rainfall in San Francisco, as measured in inches,
for the years 1967-2017. (Show all work. Not Just the
answer.)
Season Rainfall (in Inches)
Frequency
Cumulative Relative Frequency
0 - 9.99
1
10 - 19.99
22
20 - 29.99
0.84
30 - 30.99
0.98
40 - 40.99
1.00
Total
50
(a) Why is it appropriate to use a grouped frequency distribution
for this data?
(b) Complete the frequency table with frequency...
Consider that the life spam, in weeks, of a transistor has a gamma distribution with parameters...
Consider that the life spam, in weeks, of a transistor has a
gamma distribution with parameters α = 4 & β=6. Find the
probability that a random transistor will last longer than 30
weeks.
Let Xl, n be a random sample from a gamma distribution with parameters a = 2...
Let Xl, n be a random
sample from a gamma distribution with parameters a = 2 and p =
20.
a) Find an
estimator , using the method of maximum likelihood
b) Is the estimator obtained in part a) is unbiased and
consistent estimator for the parameter 0?
c) Using the
factorization theorem, show that the estimator found in part a) is
a sufficient estimator of 0.
The data represents the daily rainfall (in inches) for one month. Construct a frequency distribution beginning...
The data represents the daily
rainfall (in inches) for one month. Construct a frequency
distribution beginning with a lower class limit of
0.000.00
and use a class width of
0.200.20.
Does the frequency distribution appear to be roughly a normal
distribution?
0.480.48
0
0
0
0.180.18
0
0.180.18
0
0.020.02
0.220.22
0.450.45
0
0
0.240.24
0
0.290.29
0
0.540.54
0
1.391.39
0
0
0.190.19
0
0.010.01
0
0.260.26
0
0.210.21
0
The frequency distribution shows the average seasonal rainfall in California measured in inches Please complete the...
The frequency distribution shows the average seasonal rainfall
in California measured in inches
Please complete the chart (frequency and cumulative relative
frequency) CRF to two decimal points
Rainfall
Frequency
Cumulative Relative Frequency
0
-9.99
2
10 –
19.99
25
20 -
29.99
0.88
30 -30.99 0.98
40 –
40.99
1.00
Total
50
I would like a clear understanding of where the values come from
to complete this chart. I have seen a couple of answers that do not
clearly explain...
a.) Viscosity measurements for a certain petroleum fraction can be modelled using a normal distribution with...
a.) Viscosity measurements for a certain petroleum fraction can
be modelled using a normal distribution with a mean of 41 and a
standard deviation of 7. The 99th percentile of this distribution
is
b.) Suppose X has a normal distribution with mean 3 and standard
deviation 1. The 95th percentile of this distribution is
Group of answer choices
c.) United Airlines Flight 433 is a nonstop flight from Boston’s
Logan airport to San Francisco International Airport. An important
factor in...
a.) Viscosity measurements for a certain petroleum fraction can be modelled using a normal distribution with...
a.) Viscosity measurements for a certain petroleum fraction can
be modelled using a normal distribution with a mean of 41 and a
standard deviation of 7. The 99th percentile of this distribution
is
b.) Suppose X has a normal distribution with mean 3 and standard
deviation 1. The 95th percentile of this distribution is
Group of answer choices
c.) United Airlines Flight 433 is a nonstop flight from Boston’s
Logan airport to San Francisco International Airport. An important
factor in...
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