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1. A box contains two balls, either of which can be red or yellow. At each stage, a ball is chosen at random and replaced with a ball of the opposite colour. Let Xn be the number of red balls in the box at time n. Find the transition matrix.
2. (Random walk with absorbing barriers) Consider a random walk on four consecutive points 1, 2, 3, 4 on a line. Starting at either 2 or 3, the process moves right with probability 2/3 or left with probability 1/3. Whenever the process gets to either 1 or 4, it remains there forever. Classify the four states as to recurrent or transitive, and for each pair (i, j) of transitive states find the expected number of times the process will be in j starting from state i.
evaluate the practice of altering the alpha level so that a two-tailed test will have a 5 rejection region on both
Construct a 95% confidence interval estimate for the proportion of Americans who decided what to make for dinner either at the last minute or that day.
Determine the coefficient of determination R 2 . Determine standard error of the estimate s e .
Given f(x,y)=x3+3xy2-3x2-3y2+4. Find all critical points of f and find extreme values (maxima and minima) and saddle points of f.
The correlation coefficient between the number of casualties and the number of deaths per accidents is 0.5. Compute the expectation and variance of the total number of deaths and casualties during a year.
The average efficiency of the sample is calculated to be 91.0% and the standard deviation of the sample is 0.8%. If we want to cut the confidence interval by one-half, how many more motors should be tested?
Find a 99% confidence interval for the population mean number of weekly miles.
normal distribution if the mean per capita income in the u.s. is 39000 and the standard deviation is 5000 - what
the mean and standard deviation on a calculus mid term are 55 and 16 points while they are 65 and 22 on the final. if a
For each mutual fund, find an interval in which you would expect 95.44 percent of all yearly returns to fall. Assume returns are normally distributed.
recent difficult economic times have caused an increase in the foreclosure rate of home mortgages. statistics from the
Use any method to decide whether to rejects or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim.
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