ID: 18387Nhận biết (M1) A cellular telephone company is upgrading its network to a new transmission system one area at a time, but they do not announce where the upgrades take place. You have the task of determining whether certain areas have been upgraded. You have decided to use an application in your smartphone to measure the ping time (how long it takes to receive a response to a certain message) in each area. The new system is faster than the old one. It has on average shorter ping times.
The ping time, in milliseconds, of the new transmission system is the exponential random variable with expected value of 60 milliseconds. The ping time of the old system is the exponential random variable with expected value of 120 milliseconds. The null hypothesis of a binary hypothesis test is : "The transmission system is the new system". The alternative hypothesis is : "The transmission system is the old system". The probability of a new system is . The probability of an old system . A binary hypothesis test measures milliseconds, the ping time of one ping test. Based on the observation of ,
a) Write and , the likelihood functions of given and , respectively.
b) Design the maximum a posteriori probability (MAP) hypothesis test.
c) Find the total probability of error of the hypothesis test.
Đáp án đúng:
A cellular telephone company is upgrading its network to a new transmission system one area at a time, but they do not announce where the upgrades take place. You have the task of determining whether certain areas have been upgraded. You have decided to use an application in your smartphone to measure the ping time (how long it takes to receive a response to a certain message) in each area. The new system is faster than the old one. It has on average shorter ping times.
The ping time, in milliseconds, of the new transmission system is the exponential random variable with expected value of 60 milliseconds. The ping time of the old system is the exponential random variable with expected value of 120 milliseconds. The null hypothesis of a binary hypothesis test is : "The transmission system is the new system". The alternative hypothesis is : "The transmission system is the old system". The probability of a new system is . The probability of an old system . A binary hypothesis test measures milliseconds, the ping time of one ping test. Based on the observation of ,
a) Write and , the likelihood functions of given and , respectively.
b) Design the maximum a posteriori probability (MAP) hypothesis test.
c) Find the total probability of error of the hypothesis test.
để xem lời giải của câu hỏi này
Câu hỏi cùng chủ đề
Chưa có câu hỏi