Problem 5. The number of orders per week, X, for radios can be assumed to have...
Solve without using Poission Table Problem 5. The number of orders per week, X, for radios can be assumed to have a Poisson distribution with parameter 35. (a) Find PX 35) and PIX 25) (b) If the number of radios in the inventory is 38, what is the probability of a shortage occurring in a week?
Suppose the number of births that occur in a hospital can be assumed to have a Poisson distribution with parameter-the average birth rate of 1.8 births per hour. What is the probability of observing at least two births in a given hour at the hospital?
Suppose the number of spam calls a person receives per day can be assumed to follow a Poisson distribution with parameter λ=2. What is the probability that Jacob will receive at least two spam calls in a day? Show your steps in calculating your answer
The number of accidents occurring per week on a certain stretch of motorway has a Poisson distribution with mean 24 Find the probability that in a randomly chosen week, there are between 3 and 6 (both inclusive) accidents on this stretch of motorway O 0.419 O 0.4303 O 04660 O 0534
Suppose a professor gets 3 visitors per week on average. Let the random variable X be the number of visitors the professor gets during a certain week. a) What type of distribution does X have? ANS: Poisson Distribution b) What. is the probability mass function, f(x)? What is E(X)? What is V(X)? c) What is the probability that this teacher receives betweeen 2 and 5 visitors this week?
3. Assume that X is the number of large earthquakes (with magnitude 2 7.5) occurring in each year. A statistician suggested that X follows a Poisson distribution with parameter ?. A Poisson distribution with parameter ? has expectation ? and variance ?. Suppose a data set 1,22,.,^n is the realization of a random sample Xi,..., Xn from this distribution. One can use either ? 1-X, or ?2-1 ?21 (Xi-%)2 to estimate the parameter ?. (a) Find Eli21 (b) Are both...
Suppose the number of patients per week that visit a health center follows a Poisson distribution with a rate of 300 patients per week. Let the random variable X count the number of patients per week that visit the health center. A) State the distribution of the random variable defined above B) Compute the probability that during a randomly selected week exactly 280 patients visit the health care center C) Compute the probability that during a randomly selected week at...
Problem 4. The number of murders in Gotham on any given week is assumed to be Poisson with unknown mean λ, with different weeks independent. (a) We observe there were 2 murders one week. What is the value of λ for which this is most likely? (b) we observe for a second week, and there is murder. What is the value of λ for which these observations are most likely? (c) Generalize the above to observations a1,... ,ak over k...
Poisson Distribution Question Problem 2: Let the random variable X be the number of goals scored in a soccer game, and assume it follows Poisson distribution with parameter λ 2, t 1, i.e. X-Poisson(λ-2, t Recall that the PMF of the Poisson distribution is P(X -x) - 1) e-dt(at)*x-0,1,2,.. x! a) Determine the probability that no goals are scored in the game b) Determine the probability that at least 3 goals are scored in the game. c) Consider the event...
1. Let X be the number of homes sold per week by a group of realtors. The table lists the probability distribution of X. Find the mean and standard deviation of X. X 0 1 2 3 4 5 P(X) .17 24 19 18 .14 .08