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If the random variable T is the time to failure of a commercial product and the values of its probability density and distribution function at time t are (t) and F(t), then its failure rate at time t is given by Thus, the failure rate at time t is the probability density of failure at time t given that failure does not occur prior to time t.
(a) Show that if T has an exponential distribution, the failure rate is constant.
(b) Show that if T has a Weibull distribution, the failure rate is given by αβt β-1.
A medical researcher estimates that no more than 55% of the U.S. adults eat breakfast every day. In a random sample of 250 U.S. adults, 56.4% say that they eat breakfast every day.
according to data from the environmental protection agency the average daily water consumption for a household of four
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A United Nations report shows the mean family income for Mexican migrants to the United States is $27,000 per year. A FLOC(Farm Labor Organizating Committee) evaluation of 25 Mexican family units reveals a mean to be $30,000 with a sample standard..
Explain which parts of the sample space are being double counted on both sides of this equation and which parts are being counted once.
Perform a significant test to assess whether there is an association between mortality from cirrhosis of the liver and duration of employment in the group hired after 1945. Report a p-value.
an elevator in a building starts with 6 people and stops at 8 floors. assuming that all permutations of the passengers
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In random samples of 12 from each of two normal populations, we found the following statistics: Describe what happens when the sample standard deviations get larger.
The distribution of lifetimes for a certain type of light bulb is normally distributed with a mean of 1000 hours and a standard deviation of 100 hours. Find the 33rd percentile of the distribution of lifetimes.
Develop the estimated regression line. Jensen expects to use the machine 30 hours per week, develop a 95% prediction interval for the company's annual maintenance expense.
for a normal distribution identify the z-score location that would seperate the distribution into 2 sections so that
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