Can you help me with this question Professor? You are waiting for a bus to take you home. There are two buses you can take to get home: red buses arrive at an average rate of 4 per hour, and blue buses arrive at a rate of 5 per hour. You always take whichever bus comes first.determine [a] what is the average time you wait before catching a bus
I am not good at math but here is my attempt: Let X1 =number of people in first 10 min time interval, X2 = number of people in the rest (50 min) P(X1 + X2 >= 35 l X1 = 8) // this basically describes the question Definition of conditional probability: P (A l B ) = P (A, B)/P(B) so, P(X1 + X2 >= 35 l X1 = 8) = P(X1 + X2 >= 35 l X1=8 , X1 = 8) / P(X1 = 8) Now, memoryless properties P(A, B) = P (A) * P (B) P(X1 + X2 >= 35 l X1 = 8) = P(X2 >= 35-8) * P( X1=8) / P(X1 = 8) = P (X2>=27)
the answer to the last question needs a table or does one have to calculate from 26 down to 0? of course that cant be done but is that the general rule for answering such a question?
One does need to calculate each of the probabilities from 0 to 26. This is where a language like R can be helpful. The ppois function calculates this quantity.
First 3 are good and the last one is the best, interesting and entertaining. Cleared all doubts. Thank you sir.
Thank you for explain this.
Part d is really interesting. Thank you so much professor.
thanks a lot sir.. you are a good teacher..
Clear and helfpul explanation! Thank you!
Can you help me with this question Professor? You are waiting for a bus to take you home. There are two buses you can take to get home: red buses arrive at an average rate of 4 per hour, and blue buses arrive at a rate of 5 per hour. You always take whichever bus comes first.determine [a] what is the average time you wait before catching a bus
thanks so much :) was totally lost before watching this
thank you so much professor for the clear explanation
Can't you use the definition of conditional probability to solve part d)? if so, how would you do it? Ty
peru laye yelara vechrukkan
I am not good at math but here is my attempt:
Let X1 =number of people in first 10 min time interval, X2 = number of people in the rest (50 min)
P(X1 + X2 >= 35 l X1 = 8) // this basically describes the question
Definition of conditional probability:
P (A l B ) = P (A, B)/P(B)
so,
P(X1 + X2 >= 35 l X1 = 8) = P(X1 + X2 >= 35 l X1=8 , X1 = 8) / P(X1 = 8)
Now, memoryless properties
P(A, B) = P (A) * P (B)
P(X1 + X2 >= 35 l X1 = 8) = P(X2 >= 35-8) * P( X1=8) / P(X1 = 8)
= P (X2>=27)
Yes, the nice memoryless property is playing the trick here.
I feel using conditional probability may be done, but not at all required due to the memory loss property of Poisson distribution.
the answer to the last question needs a table or does one have to calculate from 26 down to 0? of course that cant be done but is that the general rule for answering such a question?
One does need to calculate each of the probabilities from 0 to 26. This is where a language like R can be helpful. The ppois function calculates this quantity.
thanks sir
The R statement is the code for Rstudio Rscript???