Researchers use Elisa to test for Lyme disease. Lyme disease infects 0.0009 of the US population each year. The test has a detection rate of 0.98 and a false positive rate of 0.2.

a. What is the probability of a positive test?

b. What is the probability that a person with a positive result actually has Lyme disease?

Write a python code that uses the Euler Implicit method to approximate/plot the solutions to each of the following initial-value

1. y′=−ty+4t/y, 0 ≤ t ≤ 1, y(0)=1, with h=0.1
2. y′=y2+yt, 1 ≤ t ≤ 3, y(l)=−2, with h=0.2

Due to political turbulences in Hong-Kong and the extensive protests consumers’ confidence has deteriorated in the island. The marginal propensity to consume has declined from 0.8 to 0.6. a. Use the consumption model to asses the effects of the decline in MPC on overall consumption. Use the model and the graphs. Explain.

b. How it will affect overall aggregate demand? Use the AD model with positive slope (model, graph and explanation)

Suppose you are interested in insuring a car stereo for $600 against theft. An insurance company charges a premium of $80 for coverage for 1 year, claiming an empirically determined probability of 0.8 that the stereo system will be stolen some time during the year.

(a) What is the insurance company's expected profit?

(b) What is your expected return from the insurance company if you take out this insurance?

Assume that you are using a two-factor APT model to find the expected return on a well-diversified portfolio Q that promises an expected return of 18%. The relevant factor portfolios, their betas, and their factor risk premiums are shown in the table below. The assumed risk-free rate is 3.5%.

What is the arbitrage strategy?

If 1 grams of sodium bicarbonate are decomposed, determine the combined mass loss (in grams) of water and carbon dioxide that are produced. When a 1.08g mixture of sodium chloride and sodium bicarbonate were heated for several minutes in a crucible and the mass after the first 3 heating intervals remained 0.8 grams.

What is the combined mass loss of water and carbon dioxide per gram on sodium bicarbonate?

There are four independently working machines in a hall, which do not fail in a certain period of time with the probabilities 0.9, 0.95, 0.8 or 0.85.
You calculate the probability of that in that period
a) all four machines are working b) no machine is working
c) exactly one machine works d) exactly two machines work
e) exactly three machines are working f) at least one machine is working!

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 130 engines and the mean pressure was 5.2 lbs/square inch. Assume the standard deviation is known to be 0.8. If the valve was designed to produce a mean pressure of 5.4 lbs/square inch, is there sufficient evidence at the 0.1 level that the valve performs below the specifications?

State the null and alternative hypotheses for the above scenario.

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Calculate that volumes of each stock solution you will need to assemble the following cysteine-detection reaction: 30 mM TEA, 15 mM DTNB, 75 µM cysteine in a 0.8 mL total volume. Stock concentrations are 0.5M TEA, 100 mM DTNB, and 1 mM cysteine. Don’t forget to include the volume of water you will need to reach the final total volume.

1. In a random sample, 10 employees at a local plant were asked to compute the distance they travel to work to the nearest tenth of a mile. The data is listed below.

1.1 5.2 3.6 5.0 4.8 1.8 2.2 5.2 1.5 0.8

a) Calculate the mean, median and the mode of the data.

b) Based on these numbers, what is the shape of the distribution?

c) Compute the range, standard deviation and variance of the data.