Let the probability distribution of random variable X be P(X= k) k! , k = 0, 1, 2, I then EX2 - ()
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Let X has a pmf
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- A delivery truck travels from point A to point B and back using the same route each day. There are four traffic lights on the route. Let X1 denote the number of red lights the truck encounters going from A to B and X2 denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (X1, X2) is given by Please show complete solution.Q/C/ If the disjoint events A and B such that P(B)=1/3 , then the value of P(Bn A) is------.Random variable X has the binomial distribution with n=100 and p=0.25. By using binomial probability table, find a)p(x<20) b)p(x<=15) c)p(20<x<30)
- Cars arrive at a vehicle equipment inspection station according to a Poisson Process with rate a = 8 per hour Suppose that the probability is p 0.3 that an arriving car will have no equipment violations (a) What is the probability that exactly 8 cars arrive during the hour and all 8 have no violations? (b) For any fixed number x > 8, what is the probability that x arrive during the hour of which 8 have no violation? (c) What is the probability that 8 "no-violation" cars arrive during the next hour?An average of 1 package is sent to a server in 1 second. The server, on the other hand, prepares a document using the 5 packages received. The time between packets is modeled as an exponential random variable. Let X be a random variable expressing the time it takes the server to prepare a document. The time taken to prepare a document; a) Find the probability that it is more than 10 seconds.(with detail) b) Find the probability that it is between 5 seconds and 10 seconds. (with detail)let Xxx Xz A randomsample that follows a normat exponential ExpC@), The Probability distribution '- ExP(no) 2 -ExP (n/0) Not in Ahe answer
- The time that a butterfly lives after emerging from its chrysalis can be modelled by a random variable T, the model here taking the probability that a butterfly survives for more than t days as 36 P(T >t) GE7, t>0. (6+t)² » For these problems, please ensure your answers are accurate to within 3 decimals. Part a) What is the probability that a butterfly will die within 6 days of emerging? Part b) If a large number of butterflies emerge on the same day, after how many days would you expect only 6 % to be alive? Part c) Calculate the mean lifetime of a butterfly after emerging from its chrysalis.Please help!!Is it true ore false