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Poisson probabilities:
Let Pn(t) be the probability that a Poisson process with parameter λ has n events in an interval of length t. Let h denote a very small interval of time (like ?t).
(a) Argue that
(b) Substitute expressions for P1(h) and P0(h).
(c) Let h → 0 and derive a differential equation involving Pn(t), Pn(t), and Pn-1(t).
(d) Try a solution of the form Pn(t) = cnt ne-λt and evaluate cn.
A family made an investment for 1 year that earned $7.50 simple interest. If the principal had been $25 more and the interest rate 1% less, the interest would have been the same. Find the principal and the rate.
Choose the correct statement concerning the P-value for this test.
The strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from a circular cylindrical log of radius r.
Two poles are set a = 10 feet apart, but the point of attachment P for the rope is yet to be determined. If the total walk is to be 65 feet, determine the distance from P to the ground.
A tank in the shape of right circular cylinder of diameter 10 ft is lying on its side. The tank is half full of oil that has weight density 60 lb/ft3. Find the force exerted by the oil on one end of the tank.
Looking at the Histogram, what would you say about the shape of the distribution of compressive strengths? Do the compressive strengths seem to be distributed symmetrically about the mean or are alloys with relative large or small expense ratios?..
Given this information, if a sample of 36 independent sales representatives is selected, what is the probability that the mean of the sample will exceed $130,000?
Finally, draft a sample press release for the company addressing the recall and how the company intends to manage quality issues?
Two marbles are drawn without replacement from a box with 3 white, 2 green, 2 red, and 1 blue marble. Find the probability.
Assume the readings on a thermometers are normally distrubuted with a mean of 0 degree C and a standard deviation of 1.00 degree Celsius. Find the proabilitys that a randomly selected thermometer read leass than 1.43.
How much can be saved by borrowing the funds for 30 days to take advantage of the cash discount? (Remember, Suite Dreams must borrow only the net amount due after the cash discount is taken.)
An airplane is flying on a compass heading of 300 degrees at 450 mph. A wind is blowing with the bearing 205 degrees at 85 mph. Find the component form of the velocity of the airplane and find the actual ground speed and direction of the plane.
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