- #1
archaic
- 688
- 214
- Homework Statement
- In airport A, the time between the arrivals of flights coming from the UK is exponentially distributed, with ##\lambda=1## hour.
1) What is the probability that more than 5 flights arrive within 2 hours?
2) If we choose 30 separate 2 hour intervals, what is the probability that no interval is a siege of more than 5 arrivals?
3) If the probability that no flights arrive during a time interval is 0.1, what is its length?
- Relevant Equations
- $$f(x)=\lambda e^{-\lambda x}$$
1) Since I want at least ##6## flights to come within ##2## hours, then the time interval between each should be, at worse, ##2/6=1/3## hours, and the probability is ##P(X\leq1/3)=1-e^{-1/3}##.
2) The probability that at best 5 airplanes arrive at the airport is ##P(X\geq2/5)=1-P(X<2/5)=e^{-2/5}##, and since the exponential distribution is memoryless, the probability that we want is ##(e^{-2/5})^{30}##.
3) I want to find ##t## such that ##\int_0^tf(x)dx=0.1##.
2) The probability that at best 5 airplanes arrive at the airport is ##P(X\geq2/5)=1-P(X<2/5)=e^{-2/5}##, and since the exponential distribution is memoryless, the probability that we want is ##(e^{-2/5})^{30}##.
3) I want to find ##t## such that ##\int_0^tf(x)dx=0.1##.