Write in words how to read each of the following:
{x∈I ├|0<x<1┤}
{x∈R├|x≤0 or x≥1┤}
A 6.0 cm diameter horizontal pipe gradually narrows to 2.0 centimeters. When water flows through this pipe at a certain rate, the gauge pressure in these two sections is 32.0 kPa and 24.0 kPa, respectively. What is the volume rate of flow ?
(1 point) A breathalyser test is used by police in an area to determine whether a driver has an excess of alcohol in their blood. The device is not totally reliable: 7 % of drivers who have not consumed an excess of alcohol give a reading from the breathalyser as being above the legal limit, while 10 % of drivers who are above the legal limit will give a reading below that level. Suppose that in fact 14 % of drivers are above the legal alcohol limit, and the police stop a driver at random. Give answers to the following to four decimal places.
Part a)
What is the probability that the driver is incorrectly classified as being over the limit?
Part b)
What is the probability that the driver is correctly classified as being over the limit?
Part c)
Find the probability that the driver gives a breathalyser test reading that is over the limit.
Part d)
Find the probability that the driver is under the legal limit, given the breathalyser reading is also below the limit.
Let a and b be coprime integers, and let m be an integer such that a | m and b | m. Prove that ab | m
Let a and b be coprime integers, and let m be an integer such that a | m and b | m. Prove that ab | m
Find a 95 confidence interval for based on inverting the test statistic statistic .
For our data we have
Therefore it can be proven that the MLE for is given by
To find the confidence interval I should invert the test statistic .
The most powerful unbiased size test for testing
where has acceptance region
Substituting my problem (I think) we get that the most powerful unbiased size test for testing
has acceptance region
or equivalently,
Substituting we obtain
This means that my confindence interval is defined to be
But I can't seem to find anything concrete and I feel that I've made mistakes somewhere. What to do?