Дайте ключ к задаче ( мат-ка, статистика)

[germiona]

Не прошу ответов. Не могу понять, как решить задачи.
ЛамбдаТ (Пойзон), не получается ни в екселе, ни на тех формулах(таблицах), что у меня есть( вернее я не думаю, что я иду по правильному пути решения)ю Для первой задачи мой ответ 19.2. Но это просто гранд тотал. Препод нас нагло бросил ( квиз дедлайн на спринг брейке). В книжке ничего нет. дайте плиз подсказку. Решать не надо. я сама хорошо решаю, когда знаю, что от меня требуется


A transportation engineer is interested in testing whether the arrivals of automobiles at an intersection are described well by a poisson distribution. A monitoring station was set up and counts of the number of automobiles arriving in 1 minute intervals were recorded as follows
automobiles 1-minute intervals

0 14

1 19

2 27

3 23

4 13

Based on this information, calculate the estimate of mu (lambda t) that could be used in conducting a goodness of fit test for a poisson distribution. Enter your response to two decimals (i.e. 12.12)





Question 6 (1 point)
A transportation engineer is interested in testing whether the arrivals of automobiles at an intersection are described well by a poisson distribution. A monitoring station was set up and counts of the number of automobiles arriving in 1 minute intervals were recorded as follows
automobiles 1-minute intervals

0 30

1 91

2 131

3 136

4 101

5 58

6 32

7 15

8 6



Based on this information, calculate the expected frequency for 8 or more automobiles that would be used in conducting a goodness of fit test for a poisson distribution. Enter your response rounded to one decimal (i.e. 12.1). Do not round intermediate calculations. (Check figure, mu=3)





Question 7 (1 point)
A transportation engineer is interested in testing whether the arrivals of automobiles at an intersection are described well by a poisson distribution. A monitoring station was set up and counts of the number of automobiles arriving in 1 minute intervals were recorded as follows
automobiles
1-minute intervals

0 30

1 91

2 131

3 136

4 101

5 58

6 32

7 15

8 6



Based on this information, determine the critical value of the test statistic, Chi-square, that would be used in conducting a goodness of fit test for a poisson distribution. Assume Ho: Distribution of auto arrivals is poisson with lambda t unknown (degrees of freedom equal k-2 as the population parameter, lambda t, must be estimated from the sample). Use alpha=0.05 and enter your response to four decimals (i.e. 12.1234) as shown in the table in the textbook.





Question 8 (1 point)
A transportation engineer is interested in testing whether the arrivals of automobiles at an intersection are described well by a poisson distribution. A monitoring station was set up and counts of the number of automobiles arriving in 1 minute intervals were recorded as follows
automobiles 1-minute intervals

0 30

1 91

2 131

3 136

4 101

5 58

6 32

7 15

8 6



Based on this information and assuming the expected frequency for 7 automobiles is 12.96241887, calculate the amount that would be contributed to the total value of Chi-square for this event (7 cars arriving in a one-minute interval). Enter your response rounded to four decimals (i.e. 12.1234).

[germiona]

у что никто не знает? Как почитаешь форум, так все в бизнесс школах учатся, крутые такие, а здесь бизнесс статистика андеградуейт. Я все задачи решила, кроме первой. ну не знаю я. как ее решать. Ау, МБАшники, вас же послушать. вы все А получаете по всем предметам, не верю, что у вас статистики нету в программе. Ну даетй ключ, ПЛИЗЗЗЗЗ!!!!!!

[Veselchak U]

dup

[Veselchak U]

Germiona

I didn't quite get the table in your problem. So can you describe it in more details?

[germiona]

Table
automobiles 1-minute intervals

0______________________________ 14

1 ______________________________ 19

2 _________________________________ 27

3___________________________________ _____________23

4 ________________________________________________13

To est ( sorry za translit) 4 auto bilo v 1 min interval 13 raz and so on. Mu is equal Lambda *t . Eto Poisson distribution. Mne nado naiti Mu. But how can I get lambda and t from the data what I have? I've tried to get z for every outcome, and then get chi-square(after getting expected outcome and using formula (O-E)^2/E)Where O-observed, E-expected frequency). But chi-square is not a mu. Or is it? I'm totally lost. I do not understand what Mu has to do with this.

[Centimorgan]

germiona,

В вашем случае события следуют Пуассоновскому процессу с постоянной интенстивностью. Это означает что колличество событий в интервале [t1,t2) имеет Пуассоновское распределение Pr(N([t1,t2)) = n) = mu^n*e^(-mu)/n!,
где mu = lambda*(t2-t1)

В вашем случае все упрощается, потому что t2-t1 = 1 - интервалы всегда одноминутные. Поэтому-то mu = lamda*t. Для того, чтобы посчитать lambda (оно же mu) вам надо просто взять среднее арифметическое "counts" в каждом интервале. Ну а потом уже подставлять полученное lambda формулу Пуассоновского распределения, чтобы получить "expected counts".

[germiona]

Спасибо.
Сейчас попробую ваш совет.

[IVA]

1. You have a Poisson Process, so your mu ( expected value of X) is a point estimator for (lambda*T), where T=1
mu = [sum (X_i * frequency_i)] / n
where X_i is a value of your variable x=0, 1, ..., 4 i = 1, ..., 5
n = sum(frequancy_i)
Answer: 2.02

2. You were asked to calculate 8+ expected value, that means for X = 8, 9, ..., infinity.
So it makes sence to do n * [1 - sum(expected_probability_i)], where
i = 1, ..., 7

3. Find chi-square (0.05) with 9-2=7 degrees of freedom

4. [(observed_7 - expected_7)^2]/expected_7

[germiona]

1. You have a Poisson Process, so your mu ( expected value of X) is a point estimator for (lambda*T), where T=1
mu = [sum (X_i * frequency_i)] / n
where X_i is a value of your variable x=0, 1, ..., 4 i = 1, ..., 5
n = sum(frequancy_i)
Answer: 2.02

2. You were asked to calculate 8+ expected value, that means for X = 8, 9, ..., infinity.
So it makes sence to do n * [1 - sum(expected_probability_i)], where
i = 1, ..., 7

3. Find chi-square (0.05) with 9-2=7 degrees of freedom

4. [(observed_7 - expected_7)^2]/expected_7

Вчера сдала квиз, радует, что у нас ответы сошлись:)))