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The number N of earthquakes in a highly seismic area follows a Poisson dis- tribution with...
Let X1,..., Xn and Yi,..., Ym be two independent samples from a Poisson dis- tribution with...
Let X1,..., Xn and Yi,..., Ym be two independent samples from a Poisson dis- tribution with parameter X. Let a, b be two positive numbers. Consider the following estimator for A: Y1 X1 Xn . Ym b n m (a) What condition is needed on a and b so that X is unbiased? (b) What is the MSE of A?
3. Assume that X is the number of large earthquakes (with magnitude 2 7.5) occurring in...
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...
please help me! Thanks in advance :) 5. Let N be a Poisson random variable with...
please help me! Thanks in advance :)
5. Let N be a Poisson random variable with parameter λ Suppose ξ1S2, is a sequence of 1.1.d. random variables with mean μ and variance σ2, independent of N. Let SN-ξι 5N. Determi ne the me an and variance of Sw. 6. Let X, Y be independent random variables, each having Exponential(A) distribution. What is the conditional density function of X given that Z =
1. Let {x, t,f 0) and {Yǐ.12 0) be independent Poisson processes,with rates λ and 2A, respectivel...
1. Let {x, t,f 0) and {Yǐ.12 0) be independent Poisson processes,with rates λ and 2A, respectively. Obtain the conditionafdistributiono) Moreover, find EX Y X2t t given Yt-n, n = 1,2. 2, (a) Let T be an exponential random variable with parameter θ. For 12 0, compute (b) When Amelia walks from home to work, she has to cross the street at a certain point. Amelia needs a gap of a (units of time) in the traffic to cross the...
Recall that a discrete random variable X has Poisson distribution with parameter λ if the probability...
Recall that a discrete random variable X has Poisson
distribution with parameter λ if the probability mass function of
X
Recall that a discrete random variable X has Poisson distribution with parameter λ if the probability mass function of X is r E 0,1,2,...) This distribution is often used to model the number of events which will occur in a given time span, given that λ such events occur on average a) Prove by direct computation that the mean of...
The number of medical emergency calls per hour has a Poisson distribution with parameter λ. Calls...
The number of medical emergency calls per hour has a Poisson distribution with parameter λ. Calls received at different hours are considered to be independent. Emergency calls X1 ,…, Xn for n consecutive hours has the same parameter λ. a) What is the distribution of Sn = ∑ Xi ? b) Provide Normal approximation for the distribution of Sn . c) Provide maximum likelihood estimation of λ. Calculate variance and bias of MLE. d) Calculate Fisher information and efficiency of...
STA 2171 HW3 Page 3 of 12 2. We know under certain conditions that the Normal...
STA 2171 HW3 Page 3 of 12 2. We know under certain conditions that the Normal distribution approximates the Bino- mial distribution. But the Normal distribution approximates another important discrete distribution: the Poisson distribution. The Poisson distribution is a one-parameter distribution frequently used to model the number of events that occur over a specified time period. For example, if we are interested in the modeling the number of babies born in a particular hospital during one day, then we might...
Conditional expectation. Question 2 (10.0 marks) Previous 1 2 Validate Mark Unfocus Help ndependently or the Suppose the number o calls attempte per hour to a telephone exchange has Posso tributio...
Conditional expectation.
Question 2 (10.0 marks) Previous 1 2 Validate Mark Unfocus Help ndependently or the Suppose the number o calls attempte per hour to a telephone exchange has Posso tribution with mean Suppose there is only 80% chance that an attempted call is connected a other calls connected. Let X be the number of calls that are connected in an hour. We ask you to find the mean and variance of X. In reality, this is mainly a theory...
need to check my work. Just need B and C Problem 2. Recall that a discrete...
need to check my work. Just
need B and C
Problem 2. Recall that a discrete random variable X has Poisson distribution with parameter λ if the probability mass function of X is fx (x) = e-λ- XE(0, 1,2, ) ar! This distribution is often used to model the number of events which will occur in a given time span, given that λ such events occur on average a Prove by direct cornputation that the mean of a Poisson randoln...
1. The random variable X follows a normal distribution N(10,1). Using the provided table to find...
1. The random variable X follows a normal distribution N(10,1). Using the provided table to find prob( (X-10)2 4) Patients arrive at a clinic at an average rate of 300 per hour. Assume the arrival at each minute follows a Poisson distribution 2. a. b. c. Find the probability that none passes in a given minute. What is the expected number passing in two minutes? Find the probability that this expected number actually pass through in a given two-minute period.
Let X1,..., Xn and Yi,..., Ym be two independent samples from a Poisson dis- tribution with parameter X. Let a, b be two positive numbers. Consider the following estimator for A: Y1 X1 Xn . Ym b n m (a) What condition is needed on a and b so that X is unbiased? (b) What is the MSE of A?
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...
please help me! Thanks in advance :)
5. Let N be a Poisson random variable with parameter λ Suppose ξ1S2, is a sequence of 1.1.d. random variables with mean μ and variance σ2, independent of N. Let SN-ξι 5N. Determi ne the me an and variance of Sw. 6. Let X, Y be independent random variables, each having Exponential(A) distribution. What is the conditional density function of X given that Z =
1. Let {x, t,f 0) and {Yǐ.12 0) be independent Poisson processes,with rates λ and 2A, respectively. Obtain the conditionafdistributiono) Moreover, find EX Y X2t t given Yt-n, n = 1,2. 2, (a) Let T be an exponential random variable with parameter θ. For 12 0, compute (b) When Amelia walks from home to work, she has to cross the street at a certain point. Amelia needs a gap of a (units of time) in the traffic to cross the...
Recall that a discrete random variable X has Poisson
distribution with parameter λ if the probability mass function of
X
Recall that a discrete random variable X has Poisson distribution with parameter λ if the probability mass function of X is r E 0,1,2,...) This distribution is often used to model the number of events which will occur in a given time span, given that λ such events occur on average a) Prove by direct computation that the mean of...
STA 2171 HW3 Page 3 of 12 2. We know under certain conditions that the Normal distribution approximates the Bino- mial distribution. But the Normal distribution approximates another important discrete distribution: the Poisson distribution. The Poisson distribution is a one-parameter distribution frequently used to model the number of events that occur over a specified time period. For example, if we are interested in the modeling the number of babies born in a particular hospital during one day, then we might...
Conditional expectation.
Question 2 (10.0 marks) Previous 1 2 Validate Mark Unfocus Help ndependently or the Suppose the number o calls attempte per hour to a telephone exchange has Posso tribution with mean Suppose there is only 80% chance that an attempted call is connected a other calls connected. Let X be the number of calls that are connected in an hour. We ask you to find the mean and variance of X. In reality, this is mainly a theory...
need to check my work. Just
need B and C
Problem 2. Recall that a discrete random variable X has Poisson distribution with parameter λ if the probability mass function of X is fx (x) = e-λ- XE(0, 1,2, ) ar! This distribution is often used to model the number of events which will occur in a given time span, given that λ such events occur on average a Prove by direct cornputation that the mean of a Poisson randoln...
1. The random variable X follows a normal distribution N(10,1). Using the provided table to find prob( (X-10)2 4) Patients arrive at a clinic at an average rate of 300 per hour. Assume the arrival at each minute follows a Poisson distribution 2. a. b. c. Find the probability that none passes in a given minute. What is the expected number passing in two minutes? Find the probability that this expected number actually pass through in a given two-minute period.
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