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Finding formulas for the volume enclosed by a hypersphere in n-dimensional space.
Use an n-tuple integral to find the volume enclosed by a hypersphere of radius r in n-dimensional space R^n. (Hint: The formulas are different for n even and n odd.)
What must be the odds against outcome four if there is to be no possible arbitrage when one is allowed to bet both for & against any of the outcomes?
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
A decision maker who is considered to be a risk taker is faced with this set of probabilities and payoffs. Rank the decision alternatives onthe basis of expected value.
In S(5) let pi=(245)(1354)(125). Write pi as a product of disjoint cycles and then answer the following questions. Determine pi^2, pi^5, pi^(-1).
Solving problems on venn diagram
A number (a) is called a fixed point of a function (f) if f(a)=a. Prove that, if f'(x) does NOT equal 1 for all real numbers (x), then f has at most one fixed point.
On a recent English test, students were given the names of four authors and four novels (one author one title), and asked to match each novel, with the correct author. If a student just guesses randomly, what is the probability of getting zero, on..
How many rectangles are there in a line of fifteen squares where sides are lined up with the adjacent sides touching the entire length of the side?
Formulate a linear programming model for the problem.
The equivalent impedance Z of two impedances Z1 and Z2 in parallel is given by the formula 1/Z = 1/Z1 + 1/Z2.
Using trigonometry to solve a Right triangle - Find the width of the lake.
Simple linear regression model
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