Question
In: Statistics and Probability
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.
Solutions
orchestra answered 2 years agoRelated Solutions
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.
Determine the expect value and the variance.
The lifetime of an electronic component has a Weibull distribution with parameters α=0.60 and β=2. Compute...
The lifetime of an electronic component has a Weibull
distribution with parameters α=0.60 and β=2. Compute the
probability the component fails before the expiration of a 4 year
warranty.
The maximum flood levels, in millions of cubic feet per
second, for a particular U.S. river have a Weibull distribution
with α=5/3 and β=3/2. Find the probability that the maximum flood
level for next year will exceed 0.7 million cubic feet per
second.
The lifespan of a system component follows a Weibull distribution with α (unknown) and β=1. (hint:...
The lifespan of a system component follows a Weibull
distribution with α (unknown) and β=1. (hint:
start with a confidence interval for μ)
f(x)=αβXβ-1 exp(-αXβ)
a. Derive
92% large sample confidence interval for α.
b. Find the
maximum likelihood estimator of α.
The lifespan of a system component follows a Weibull distribution with α (unknown) and β=1. (hint:...
The lifespan of a system component follows a Weibull
distribution with α (unknown) and β=1. (hint:
start with confidence interval for μ)
f(x)=αβXβ-1 exp(-αXβ)
a. Derive
98% large sample confidence interval for α.
b. Find maximum
likelihood estimator of α.
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.
Suppose a car radiator useful lifetime has Weibull distribution with β = 1.5 and the mean...
Suppose a car radiator useful lifetime has Weibull distribution
with β = 1.5 and the mean lifetime of 150,000 miles. John has just
bought a used car with 180,000 miles and original radiator which is
still good. What is the probability that it’s going to last at
least 20,000 miles more before needing replacement?
Assume that the life of an engine follows a normal distribution with an average life of 12 years and a standard deviation of 2 years
Assume that the life of an engine follows a normal
distribution with an average life of 12 years and a standard
deviation of 2 years. The seller replaces all engines that fail
during the warranty period without additional charges.a) If the manufacturer wishes to replace only 1% of the
engines it sells, what is the warranty time it must offer?b) supposes that Puerto Rico sold 30 engines, what is the
percentage of probability that more than 1 customer will claim...
A roller bearing has a 22 kN radial load applied. For a life of 18000 hours...
A roller bearing has a 22 kN radial load applied. For a life of
18000 hours at 1200 rev/min, specify the smallest suitable roller
bearing to use. Assume a rotating outer ring and provide relevant
source information for your selected bearing.
Estimation of the parameters for the Exponential and Weibull distributions. DATA SET A: 2, 14, 23,...
Estimation of the parameters for the Exponential and Weibull
distributions.
DATA SET A: 2, 14, 23, 45, 67, 75, 89, 99, 101, 123, 138, 159,
188, 201, 203
DATA SET B: 13, 24, 35+, 65, 86, 99, 109, 118+, 131, 159, 189,
207
DATA SET C: 5, 13, 34+, 46+, 55, 74, 89, 93, 104, 112+, 126,
134, 145, 159, 167+, 173, 198, 203, 226, 241
DATA SET D: 9, 14, 85, 99, 126, 155, 169+, 199, 201+, 224+, 229,...
The lifespan of a system component follows a Gamma distribution with β (unknown) and α=1. (hint:...
The lifespan of a system component follows a Gamma distribution
with β (unknown) and α=1. (hint: start with
confidence interval for μ)
f(x)=(1/βα Γ(α)) Xα-1 e-X/β
a. Derive
98% large sample confidence interval for β.
b. Find maximum
likelihood estimator of β.
a) 98% large sample confidence interval fo β is
b) MLE for β is
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