Question
In: Statistics and Probability
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.
Solutions
orchestra answered 2 years agoRelated Solutions
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 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...
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)...
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.
Consider we have a Poisson distribution with Gamma prior. If we have specified the prior Gamma(2,1)...
Consider we have a Poisson distribution with Gamma prior. If we
have specified the prior Gamma(2,1) and observed the data 1 2 1 2 2
1 2 0 2 0, what would be our point estimate by using the mean of
posterior? What is the 95% credible interval for θ?
Suppose X follows a Gamma distribution with parameters α, β, and the following density function f(x)=...
Suppose X follows a Gamma distribution with parameters α, β, and
the following density function f(x)= [x^(α−1)e^(−x/ β)]/ Γ(α)β^α .
Find α and β so that E(X)= Var(X)=1. Also find the median for the
random variable, X.
Consider the independent observations x1, x2, . . . , xn from the gamma distribution with...
Consider the independent observations x1, x2, . . . , xn from
the gamma distribution with pdf f(x) = (1/ Γ(α)β^α)x^(α−1)e
^(−x/β), x > 0 and 0 otherwise.
a. Write out the likelihood function
b. Write out a set of equations that give the maximum likelihood
estimators of α and β.
c. Assuming α is known, find the likelihood estimator Bˆ of
β.
d. Find the expected value and variance of Bˆ
(i) Consider a CMOS inverter supplied at VDD= 5V with transistor parameters of KN=KP=50µA/V2 and VTN=-VTP=1V....
(i) Consider a CMOS inverter supplied at
VDD= 5V with transistor parameters of
KN=KP=50µA/V2 and
VTN=-VTP=1V. Then consider another CMOS
inverter supplied at VDD= 10V with the same transistor
parameters. Draw the VTC of both inverters showing all regions of
operation and the middle voltage VM. Verify your results
using PSpice.
(ii) Draw the square root of the CMOS inverter
current versus the input voltage for the two CMOS inverters in
given in part (i) biased at either...
(i) Consider a CMOS inverter supplied at VDD= 5V with transistor parameters of KN=KP=50µA/V2 and VTN=-VTP=1V....
(i) Consider a CMOS inverter supplied at
VDD= 5V with transistor parameters of
KN=KP=50µA/V2 and
VTN=-VTP=1V. Then consider another CMOS
inverter supplied at VDD= 10V with the same transistor
parameters. Draw the VTC of both inverters showing all regions of
operation and the middle voltage VM. Verify your results
using PSpice.
(ii) Draw the square root of the CMOS inverter
current versus the input voltage for the two CMOS inverters in
given in part (i) biased at either...
Assume the life of a roller bearing follows a Weibull distribution with parameters β=2 and δ=7,500...
Assume the life of a roller bearing follows a Weibull
distribution with parameters β=2 and δ=7,500
hours.
Determine the probability that the bearing will last at least
8000 hours.
Verify your answer using R.
Determine the expect value and the variance.
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