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Let be a modified version of the random telegraph process. The process switches between the two states with the time between switches following exponential distributions, Also, the starting state is determined by flipping a biased coin so that
Pr(X(0)=1) = p and
Pr(X(0)=-1) = 1 - p.
(a) Find Pr(X(t)=1) and Pr(X(t)=-1).
(b) Find the mean function, μX(t).
(c) Find the autocorrelation function RX,X(t1,t2)
(d) Is given process Wss?
Use the hypergeometric formula to find this probability. The lottery commission also pays if a contestant matches 4 or 5 of the 6 winning numbers. Hint: Divide the 44 numbers into two groups, winning numbers and nonwinning numbers.
annual starting salaries for college graduates with degrees in business administration are generally expected to be
consider the model below for scheduling postal workers to 5 day shiftsminimize z mf ts wsu thm ft sw suthsubject
The statewide incidence of gonorrhea is 50 per 100,000 over a 3 month period. Is the number of gonorrhea cases in this county unusual for this time period?
A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster.
An event independently occurs on each day with probability p. Let N(n) denote the total number of events that occur on the ?rst n days, and let Tr denote the day on which the rth event occurs. (a) What is the distribution of N(n)?
Construct a 95% con?dence interval for the variance of change in heart rate. Assume that the population has a normal distribution and interpret.
For the product measure λ × λ on R2, the usual Lebesgue measure on the plane, it's very easy to show that rectangles parallel to the axes have λ × λ measure equal to their usual areas, the product of their sides. Prove this for rectangles that are..
After popping, the un-popped kernels were counted. There were 89. Construct a 90 percent confidence interval for the proportion of all kernels that would not pop.
Now that you are an adult, you decide to test one of the truisms passed along by your mother: "Cheaters never win in the end." You randomly assign a group of 20 children to either cheat or to play fair on a scavenger hunt.
The period of the orbit is 2.3 hours. The radius of the planet is 4.34 × 106 m. What would be the true weight of the satellite if it were at rest on the planet's surface?
Examine the residual files and produce appropriate residual plots to examine the assumptions. Are the Level-1 residuals normally distributed? Are the level-2 residuals multivariate normal? How do you know?
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