Let Y be the number of calls to a particular hotline within 10 min. Suppose Y is a Poisson random... Let Y be the number of calls to a particular hotline within 10 min. Suppose Y is a Poisson random variable with mean of 3. Find the probability that there are at most 4 calls given that there are already 2 calls within the 10 min.
THIS IS NOT A STRAIGHTFORWARD CONDITIONAL PROBABILITY! I'VE POSTED THIS TWICE ALREADY AND BOTH TIMES I RECEIVED AN ANSWER OF 1. THIS IS INCORRECT!
Let Y be the number of calls to a particular hotline within 10 min. Suppose Y...
Suppose the number of phone calls passing through a particular cellular relay system, follows a Poisson distribution with an average of 3 calls during a 1-min period. (A) Find the probability, p, that no call will pass through the relay system during a given 2-min period. (B) Find the probability that at least four minutes will pass before a call is passed through the relay system.
The random variable x is the number of the number of calls received by a switchboard. Suppose x follows a Poisson distribution and the average number of occurrences in 20 minutes is 2. (1) What is the probability that between 10:00 and 10:30 the switchboard will receive exactly 5 calls? (2) What is the probability that between 10:00 and 10:30 the switchboard will receive more than 2 calls but fewer than 6 calls? Need Help
5. Let X be a Poisson random variable with parameter λ 6, and let Y-min(X,12 (a) What is the p.m.f. of X? (b) What is the mean of X? (c) What is the variance of X? (d) What is the p.m.f. of Y? (e) Compute E[Y].
Suppose the number of phone calls arriving at an answering service follows a Poisson process with the rate lambda = 60 (or equivalently, the interarrival times are iid exponential random variables with mean 1 minute). a.) Let T(I,j) denote the time interval from the ith arrival the jth arrival. The correlation between T(10,50) and T(20,60) is equal to ____________. b.) The correlation between T(0,20) and T(0,60) is equal to ________________.
On average, a particular web page is accessed 10 times an hour. Let X be the number of times this web page will be accessed in the next hour. (a) What is E[X] and Var[X]? (b) What is the probability there is at least one access in the next hour? (c) What is the probability there are between 8 and 12 (inclusive) accesses in the next hour? and, Let X be a random variable with image Im(X) = (0, 1,...
A particular telephone number is used to receive both volce calls and fax messages. Suppose that 25 of the incoming calls involve fax messages, and consider a sample of incoming calis (Round your answers to three decimal places.) (a) What is the probability that at most of the calls involve a fax message? (b) What is the probability that exactly 4 of the calls involve a fax message? (c) What is the probability that at least 4 of the calls...
A particular telephone number is used to receive both voice calls and fax messages. Suppose that 25% of the incoming calls involve fax messages, and consider a sample of 25 incoming calls. (Round your answers to three decimal places.) (a) What is the probability that at most 8 of the calls involve a fax message? (b) What is the probability that exactly 8 of the calls involve a fax message? (c) What is the probability that at least 8 of...
2. (a) Die #1 has 6 sides numbered 1, . . . , 6 and die #2 has 8 sides numbered 1, . . . , 8. One of these two dice is chosen at random and rolled 10 times. Find the conditional probability that you have selected die #1 given that precisely three 1’s were rolled. (b) Let X and Y be independent Poisson random variables with mean 1. Are X − Y and X + Y independent? Justify...
The number of messages sent to a computer website is a Poisson random variable with a mean of 5 messages per hour. a. What is the probability that 5 messages are received in 1 hours? b. What is the probability that fewer than 2 messages are received in 0.5 hour? c. Let Y be the random variable defined as the time between messages arriving to the computer bulletin board. What is the distribution of Y? What is the mean of...
Suppose your hamster poops X times before noon and Y times after noon. Where X is a Poisson (2) random variable and Y is an independent Poisson(3) random variable. a. What is the expected number of poops the hamster took in a day? b. What is the probability the hamster pooped fewer than 2 times a day?