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Question: 1. Three people, A, B and C, live in the same neighborhood and use the same bus line to go to work. Each of the three has a probability of ¼ of making the 6:10 bus, a probability of ½ of making the 6:15 bus, and a probability of ¼ of making the 6:20 bus. Assuming independence, what is the probability that they all take the same bus?
2. The probability density function of a certain voltage is given by
pv(v) = ve-vU(v)
where U(v) is the unit step function.
(a) Sketch this probability density function.
(b) Sketch the distribution function of v.
(c) What is the probability that v is between I and 2?
The purpose of this problem is to illustrate the dangers of statistics, especially with respect to categorical data and the use of conditional probabilities.
What is the probability that exactly 1 of 10 cars experience breakdown: Use the Binomial Probability tables.
Use the output to compare graphically the distribution of x(t) at t = 0.5 and t = 1. Experiment with n and M to try to obtain better approximations to the known distributions
Suppose Annabelle decides to change her risk-balancing formula by eliminating the restriction that the proportion of the amount she invests s in the index fund to the amount that she invests in the Internet fund must be at least one-third. What wi..
Nowadays it is very important to reduce one's carbon "footprint" (how much carbon we produce in our daily lifestyles).
Solve the following network flow problem starting with the spanning tree shown.
Add a column to the right of the Last column. Label it "Full Name." Using spreadsheet functions or operations, populate the Full Name column using the format "Last Name, First Name."
Given a grid of size m * n, lets assume you are starting at (1,1) and your goal is to reach (m,n). At any instance, if you are on (x,y).
Solve it by using the primal simplex algorithm discussed in a previous section. Exhibit all the relevant information about the primal and dual solutions.
Write your response to the following topic.
Find the range of values of the parameter a for which the function f(x1, x2, x3) = 2x1x3 - x12 - x22 - 5x32 - 2ax1x2 - 4x2x3 is concave
The driving distance for the top 100 golfers on the PGA tour is between 284.7 and 310.6 yards (GoIfweek, March 29. 2003).
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