Question

Data indicates that the number of traffic accidents on a rainy day is Poisson with mean...

Data indicates that the number of traffic accidents on a rainy day is Poisson with mean 19, while on a dry day, it is Poisson with mean 13. Let X denote the number of traffic accidents tomorrow. Suppose that the chance it rains tomorrow is 0.6. Find(a)P(rain tomorrow|X= 15) using Bayes rule. (b)E(X).

Homework Answers

Answer #1

a)P(rain tomorrow|X= 15) using Bayes rule as consider by:

= P(X=15)

= P(X=15 and rainy day) + P(X=15 and dry day)

= (e^-19*19^15/15! ) *0.6 + ( e^-13*13^15/15!)*0.4
=   0.0650*0.6 + 0.0885*0.4

= 0.07441673

P (rain tomorrow|X= 15) = 0.0650*0.6/0.07441673

                                    =    0.5244

Therefore,

P(x =15) = 0.5244

b) E(X) as consider by:

E(x) = 19*0.6+13*0.4

        = 16.6

Therefore,

E(x) = 16.6

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Question 5. Suppose that the number of accidents in a city on a rainy day is...
Question 5. Suppose that the number of accidents in a city on a rainy day is a Poisson random variable with mean 8, on a cloudy day is a Poisson random variable with mean 5 and on a sunny day is a Poisson random variable with mean 2. If the probability that it will be rainy tomorrow is 0.4, the probability that it will be cloudy tomorrow is 0.3 and the probability that it will be sunny tomorrow is 0.3;...
The number of traffic accidents in a certain area follows a Poisson process with a rate...
The number of traffic accidents in a certain area follows a Poisson process with a rate of 1.5 per hour between 8:00 A.M. and 5:00 P.M. during the normal working hours in a working day. Compute the following probabilities. There will be no traffic accident between 11:30 AM to 12:00 PM. There will be more than 3 traffic accidents after 3:45 P.M. There will be in between 15 and 18 traffic accident during the normal working hours in a working...
The following table contains the probability distribution for the number of traffic accidents daily in a...
The following table contains the probability distribution for the number of traffic accidents daily in a small town. Complete parts​ (a) and​ (b) to the right. Number of Accidents Daily​ (X) ​P(X) 0 0.19 1 0.28 2 0.22 3 0.12 4 0.09 5 0.06 6 0.04 a. Compute the mean number of accidents per day. μ =1.98 correct b. Compute the standard deviation. **** dont know the answer below**** σ =___________ Determine the mean and standard deviation of the variable...
The following table contains the probability distribution for the number of traffic accidents daily in a...
The following table contains the probability distribution for the number of traffic accidents daily in a small town. Complete parts​ (a) and​ (b) to the right. Number of accidents daily (x) P(X) 0 0.30 1 0.37 2 0.16 3 0.07 4 0.05 5 0.04 6 0.01 a. Compute the mean number of accidents per day. b. Compute the standard deviation.
The following table contains the probability distribution for the number of traffic accidents daily in a...
The following table contains the probability distribution for the number of traffic accidents daily in a small town. Complete parts​ (a) and​ (b) to the right. Number of Accidents Daily​ (X) ​P(X) 0 0.260 1 0.340 2 0.180 3 0.090 4 0.060 5 0.040 6 0.030 a. Compute the mean number of accidents per day. μ=1.59 ​(Type an integer or a​ decimal.) b. Compute the standard deviation. σ= ​(Type an integer or decimal rounded to three decimal places as​ needed.)
A civil engineer has been studying the frequency of vehicle accidents on a certain stretch of...
A civil engineer has been studying the frequency of vehicle accidents on a certain stretch of interstate highway. Longterm history indicates that there has been an average of 1.74 accidents per day on this section of the interstate. Let r be a random variable that represents number of accidents per day. Let O represent the number of observed accidents per day based on local highway patrol reports. A random sample of 90 days gave the following information. r 0 1...
1-The number of defective components produced by a certain process in one day has a Poisson...
1-The number of defective components produced by a certain process in one day has a Poisson distribution with mean 19. Each defective component has probability 0.6 of being repairable. a) Given that exactly 15 defective components are produced, find the probability that exactly 10 of them are repairable. b) Find the probability that exactly 15 defective components are produced, with exactly 10 of them being repairable.
Please answer with method or formula used. A) Puenaa is getting married tomorrow, at an outdoor...
Please answer with method or formula used. A) Puenaa is getting married tomorrow, at an outdoor ceremony in the desert. In recent years, it has rained only 5 days each year. Unfortunately, the weatherman has predicted rain for tomorrow. When it actually rains, the weatherman correctly forecasts rain 90% of the time. When it doesn't rain, he incorrectly forecasts rain 10% of the time. What is the probability that it will rain on the day of Puenaa's wedding? B) A...
2) Airline accidents: According to the U.S. National Transportation Safety Board, the number of airline accidents...
2) Airline accidents: According to the U.S. National Transportation Safety Board, the number of airline accidents by year from 1983 to 2006 were 23, 16, 21, 24, 34, 30, 28, 24, 26, 18, 23, 23, 36, 37, 49, 50, 51, 56, 46, 41, 54, 30, 40, and 31. a. For the sample data, compute the mean and its standard error (from the standard deviation), and the median. b. Using R, compute bootstrap estimates of the mean, median and 25% trimmed...
1 the probability distribution of x, the number of defective tires on a randomly selected automobile...
1 the probability distribution of x, the number of defective tires on a randomly selected automobile checked at a certain inspection station, is given in the following table. The probability distribution of x, the number of defective tires on a randomly selected automobile checked at a certain inspection station, is given in the following table. x 0 1 2 3 4 p(x) .53 .15 .08 .05 .19 (a) Calculate the mean value of x. μx =   (a) Calculate the mean...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT