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1. Suppose we play a game where we start with c dollars. On each play of the game you either double or halve your money, with equal probability. What is your expected fortune after n trials?
2. Show that V(X) = 0 if and only if there is a constant c such that P (X = c)= 1.
3. Let X1,..., Xn ∼ Uniform(0, 1) and let Yn = max{X1,..., Xn}. Find E(Yn).
4. A particle starts at the origin of the real line and moves along the line in jumps of one unit. For each jump the probability is p that the particle will jump one unit to the left and the probability is 1-p that the particle will jump one unit to the right. Let Xn be the position of the particle after n units. Find E(Xn) and V(Xn). (This is known as a random walk.)
Index number acts as a barometer for measuring the value of money. What are the characteristics of an index number? State its utility.
Create a contingency table for this data: In a "taste test" fourteen men showed a preference for Coke an the same number showed a preference for Pepsi.
a redundant constraint is eliminated from a linear programming model. what effect will this have on the optimal
Create an accurate scatter plot of the data. This can be done by hand or using a program like Excel. Use Height as the x variable and Arm Span as the y variable. Does this graph show a linear relationship between x and y?
Please use words to describe the solution, not just symbols. (basically, explain what is going on in addition to an answer) Use a math symbol editor where appropriate.
If the power plant of this city has a daily capacity of 12 million kilowatt hours what is the probability that this power supply will be inadequate on any given day.
What percentage of bags will weigh more than 16.4 ounces? What percentate of bags will weigh less than 15.92 ounces
Suppose that the license will be awarded on the basis of a first-price auc-tion. What are the equilibrium bidding strategies? What is the expected revenue of the seller, that is, the holder of the patent?
Use Excel or SASto perform the one-way analysis of variance (ANOVA) for the data. APA format is required, and solid academic writing is expected
Peter and Ray built a bike ramp from 20 sheets of 4ft. X 8ft. plywood and propped it up on one end with some bricks. The finished ramp is rectangular. Show 3 ways they might have arranged the wood and give the measurment for each side.
A sample of 200 such candies is randomly selected. Find the mean and the standard deviation for the number of orange candies in such groups of 200.
NBC TV news, in a segment on the price of gasoline, reported last evening that the mean price nationwide is $1.50 per gallon for self-serve regular unleaded.
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