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1). Let D = {z: |z| < 1 } and find all Mobius transformations T such that T(D) = D.
2). Show that a Mobius transformation T satisfies T(0) = infinity and T ( infinity) = 0 if and only if Tz = az^-1 for some a in C ( C is complex plane).
Uniform Distribution and a 20-Sided Die, In this problem there are two ways to solve one is the largest way counting every pair of the outcome and the other is the smallest, using CDF.
A firm has two fixed resources that impose limits on its production activities. For a particular period of time it has 30 hours of resource 1 available and 80 hours of resource 2.
Given that the y-intercept of a line is (0,-5) and the slope is 1/3, find the equation of the line in slope-intercept form. What is the x-intercept?
Solving problems on venn diagram
Simple Probability, Sample Spaces, Events, A couple has three children, assume the likelihood of a boy is the same as a girl:
Find the percent of the dowels will have a diameter less than 0.56?
What is the probability of drawing three queens in a row from a deck of cards when the drawn card is returned each time?
Use Gaussian elimination with partial pivoting to find matrices L and U such that U is upper triangular, L is lower triangular with | l_ij| = j and LU = A', where A' can be obtained from A by interchanging rows.
How would I solve the characteristic equation for B and show that the eigenvalues are 0, 2 and 4? For each eigenvalue, how would I find a corresponding eigenvector?
Problems on linear regression equation
Assume S is a subset of the complex number set. Please make the explanations clear and give examples.
Sampling distribution of sample mean- key informaiton. What is the probability that the sample mean will be between 28 and 46?
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