#57, Constants of Poisson Distribution (HINDI)

[@akashmondal6949]

Thank you so much madam🙏

[@playvideos876]

Mam please answer my question Assume that cars pass under a bridge at a rate of 100 per hour and that a Poisson distribution is appropriate. a What is the probability that during a 3-minute period no cars will pass under the bridge? b What time interval is such that the probability is at least 0.25 that no car will pass under the bridge during that interval?

[@apparacademy4616]

Since on an average 100 cars paas in 60 mins. This means on an avaeragr 100/60 cars pass per minute This means on an average (100/60)*3 cars pass in 3 mins. (100/60)*3 =5 This means for 3 mins on an average 5 cars pass under the bridge. So new mean is 5 cars for 3 mins. You can calculate P(X=0) taking mean as 5 This answers your first question that what is the probability that during a 3 minute period no cars pass under the bridge

[@apparacademy4616]

For part B) We dont know the value of lamda But we know that P(X=0) >=0.25 Using this we know e^(-lambda) >=0.25 From here we can compute the value of lambda This value of lambda represents average no of cars that will pass in x mins. So now using this we know 100 cars pass in 60 mins 1 car passes in 60/100 mins Lambda car passes in (60/100)*lambda mins This solves part b)

[@playvideos876]

@@apparacademy4616 Thanks alot sir