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Suppose that the demand for a company's product in weeks 1, 2, and 3 are each normally distributed and the mean demand during each of these three weeks is 50, 45, and 65, respectively. Suppose the standard deviation of the demand during each of these three weeks is known to be 10, 5, and 15, respectively. It turns out that if we can assume that these three demands are probabilistically independent then the total demand for the three week period is also normally distributed. And, the mean demand for the entire three week period is the sum of the individual means. Likewise, the variance of the demand for the entire three week period is the sum of the individual weekly variances. But be careful! The standard deviation of the demand for the entire 3 week period is not the sum of the individual standard deviations. Square roots don't work that way!
Now, suppose that the company currently has 180 units in stock, and it will not be receiving any further shipments from its supplier for at least 3 weeks. What is the probability that the company will run out of units?
The answer to finite abelian group, Suppose that G is a finite Abelian group and G has no element of order 2. Show that the mapping g-->g^2 is an automorphism of G.
A football is thrown downward from a window in a tall building. Its position at time t in seconds is s=16t^2+32t, where s is in feet. How long to the nearest tenth will it take the ball to fall 175 feet?
Prove that if f(x) is even on [-a, a] and integrable on [0, a] where a>0, then f(x) is integrable on [-a, a] and Int([-a, a], f(x)dx) = 2*Int([0, a], f(x)dx).
The solution to minimization, The ABC small-scale industry has production facilities for two different products. Each of the products requires three different operations
Factorize and solve the given quadratic equation and Solving the given quadratic equation by using formula method
Consider a standard deck of playing cards. You randomly select a card from the deck and find that you have drawn a face card.
A random sample of size 10 bulbs is selected from the storage room, what is the probability that exactly 4 of the bulbs will have a lifetime less than 16 days?
PQR and ABC are complementary angles. And PQR is eight times as large as ABC. Determine the measure of each angle.
Write an ABEL program for a combinational logic function with five input bits N4-N0) representing an integer between 0 and 31 and two outputs M3 and M5 to indicate if the number is a multiple of 3 or 5.
Simulation of an expectation. Design a simulation exercise in R to approximate the value of E ( X^X) when X has a U [0,1] distribution. Plot the value of the approximation as the sample size goes from 1 to 10,000
Factor polynomial and state the multiplicity of each zero - Use the factor theorem to find P(x)
Find the equation of a parabola whose vertex is (0,0) and directrix is the line y=3. Find the vertex, focus, and directrix of (x-2)^2=12(y+1). Find the latus rectum and graph the parabola, making sure that all points and axis are labeled.
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