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Question: Let Nt,t=0 be a Poisson process with intensitya. Let X be a random variable, independent of the Poisson process Nt, meaning that X is independent of all the "gap times" Lkused to define Nt. You are given that X is exponentially distributed with parametera ~.
(a) Find the distribution of NX, that is, the Poisson process N that the random time t=X. That is, find P(NX=k), for each k? Z+. Hint: first compute P(NX=k), which can be expressed as a two-dimensional integral. Then write P(NX=k) =P(NX=k)-P(NX=k+ 1).
(b) Suppose that Y is another random variable independent of the Poisson process, this time with the uniform distribution on the time interval [0, b]. What is the probability that NY= 0? Hint: as a check on your answer, the probability P(NY= 0) should tend to 1 asb? 0, and it should tend to 0 asb?
Using the sample variance from the data of your own survey to estimate the population variance, specify a desired precision and calculate the sample size necessary to achieve it with 95% confidence in a future survey of the same population.
Estimate descriptive statistics for each investment via Excel. Compare the two investments. Be sure to comment on the central tendency, variability and shape of these two investments
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Create a probability model for the number of children they'll have.- Find the expected number of children.- Find the expected number of boys they'll have.
At the 1% level of significance, can it be concluded that there is a relationship between an employee's age and an employee's opinion about the new wage incentive plan? Formulate and test the appropriate hypotheses. Show every step with explanatio..
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