Question
In: Statistics and Probability
The time required to service a particular machine is an exponential random variable with mean 10...
The time required to service a particular machine is an exponential random variable with mean 10 minutes. If a repair person has 35 machines to service, compute the approximate probability that all the work can be completed in under 5 hours.
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Expert Solution
TOPIC:Application of the Central limit theorem (CLT ) for Exponential distribution.
orchestra answered 2 years agoRelated Solutions
For a particular machine, its useful lifetime (random variable T) is modeled by an exponential probability...
For
a particular machine, its useful lifetime (random variable T) is
modeled by an exponential probability density function. Given that
the expected lifetime of this machine is 10 years, find the
exponential probability density function f(t) for random variable
T
For a particular machine, its useful lifetime (random variable T) is modeled by an exponential probability...
For
a particular machine, its useful lifetime (random variable T) is
modeled by an exponential probability density function. Given that
the expected lifetime of this machine is 10 years, find the
exponential probability density function f(t) for random variable
T
Suppose X is an exponential random variable with mean 5 and Y is an exponential random...
Suppose X is an exponential random variable with mean 5 and Y is
an exponential random variable with mean 10. X and Y are
independent. Determine the coefficient of variation of X + Y
The time between successive arrivals of calls to emergency service is random variable which follows exponential...
The time between successive arrivals of calls to emergency
service is random variable which
follows exponential distribution. It was observed that on average
calls arrive to emergency
service every four minutes (1 / λ = 4min) and average number of
calls in one minute is λ = 0.25 calls/ 1 min
The probability that the time between successive calls is less
than 2 minutes is ______
The probability that the time between successive calls is less
than 2 minutes is...
Lifetime of a particular laptop is exponential random variable with average of 5 years. A company...
Lifetime of a particular laptop is exponential random variable
with average of 5 years. A company orders 100 of such laptops. Find
the probability that there are more than 20 laptops still in
operation after 6 years from the date of purchase. (Hint: First
compute the probability of one laptop still being in operation
after 6 years. That will be the probability of ”success”. Then
compute the probability that you’ve at least 20 out of 100 with
that property.)
This is the code for the LLN question iid random variable from exponential distribution with mean...
This is the code for the LLN question iid random variable from
exponential distribution with mean beta. Beta is fixed 1 for
illustration.
# Testing LLN
plot.ybar <- function(n, m = 1e5, beta = 1) {
Ybars <- rep(0,m)
for(i in 1:m) {
Y.sample <- rexp(n,1/beta)
Ybars[i] <- mean(Y.sample)
}
p <- hist(Ybars, xlim=c(0,4), freq=F,main = paste("Distribution
of Ybar when n=",n, sep=""))
}
par(mfrow = c(2,2))
for (n in c(2, 10, 50, 200)) {
plot.ybar(n)
}
Using similar code...
Suppose the waiting time between earthquakes in B is an exponential random variable. On average, B...
Suppose the waiting time between earthquakes in B is an
exponential random variable. On average, B gets a really bad
earthquake every 100 years. Given that the last really bad
earthquake was 99 years ago, compute the probability we get a
really bad earthquake within one year from now.
Answer is 0.00995
If Y is a random variable with exponential distribution with mean 1/λ, show that E (Y...
If
Y is a random variable with exponential distribution with mean 1/λ,
show that E (Y ^ k) = k! / (λ^k), k = 1,2, ...
Q1. (A) Explain the exponential random variable and normal random variable with at-least ten examples in...
Q1.
(A) Explain the exponential random variable and normal random
variable with at-least ten examples in real life? In which
situation we prefer normal random variable instead of exponential
variable?
(B) Find the Mean, variance and cumulative density function for
following probability density function as: (state your results in
detail computation)
f(w)=10
e-10w ; 0≤w≤∞
Suppose the time between buses at a particular stop is a positively skewed random variable with...
Suppose the time between buses at a particular stop is a
positively skewed random variable with an average of 60 minutes and
standard deviation of 6 minutes. Suppose the time between buses at
this stop is measured for a randomly selected week, resulting in a
random sample of n = 36 times. The average of this sample,
X, is a random variable that comes from a specific probability
distribution.
(a)Which of the following is true about the distribution of mean...
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