4.. ( )The average number of decays in a Poisson process is two decays per second. What is the probability that there will be at least two decays in a randomly selected 1-second interval?
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- Q1Suppose that earthquakes occur according to a Poisson process with rate λ = 0.2 per day. (a) What is the probability that there will be 2 or fewer earthquakes in April? (b) Starting from now, what is the probability that the second earthquake will occur within a week?The time between successive calls to a corporate office is exponentially distributed with a mean of 10 minutes. Assume that the times between successive calls are independent of each other. Thus, the calls arrive according to a Poisson process. Determine x such that the probability that there are no calls within x minutes is 0.005.
- A radioactive source is observed during 7 time intervals each of ten seconds in duration. The number of particles emitted during each period is counted. Suppose that the number of particles emitted, say X, during each observed period has a Poisson distribution with parameter 5.0.(That is, particles are emitted at the rate of 0.5 particles per second.)(a) What is the probability that in each of the 7 time intervals, 4 or more particles are emitted?(b) What is the probability that in at least 1 of the 7 time intervals, 4 or more particles areemitted?Could you solve (i), (ii), (iii)? Thank you.Suppose that in a city, the number of murders can be approximated by a Poisson process with λ = 0.33 per month. (a) Find the probability of k murders per year for k ≥ 0 € Z. What is the most probable number of murders? (b) What is the probability of two murders in one week?
- In a given time series: Y1, Y2, Y3, ..., we expect there is: **** OA. autocorrelation in the Y's. B. heteroscedasticity. Oc. no correlation between any two Y's. D. none of the above.Could you solve the questions in the screenshot? If you are going to use a program, please use R only Thank you.Let (a) be a white noise sequence with mean zero and variance of 4. Is the following processes stationary? Justify your answer. X=a1+a, when t is odd, and X=a-a-1 whent is even. Edit View Insert Format Tools Table