# How do i calculate the following properties of waiting time for bus? (almost finished, very urgent to me)

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he waiting time in minutes for a bus in a certain station(from getting to the station until the bus arrival) is a random exponential variable with a mean of 10. But if the the traffic is busy, then its mean is 20. The probability that the traffic will be busy when waiting for the bus is 0.18.

1)what is the probability that a man that arrives in random time will wait longer than 15 minutes?

2)if a man waits longer than 15 minutes,what is the probability that the traffic is busy?

3)if a man comes in a random day and after 8 minutes still waiting, what is the probability he'll have to wait for not longer than 15 minutes?

what i already did:

1) expected variance: 14.76, expected mean= 11.8. using z score the result is 0.2.

2)defined the events a - being late, b−x>15.p(a)=0.2, #P(B)=P(B|A)P(A)+P(B|A^c)P(A^c) =\exp(-\frac{15}{20})\cdot 0.18+\exp(-\frac{15}{10} )\cdot 0.82# and then used bayes #p(a|b)=(p(b|a)p(a))/(p(b))# (couldn't finish it unfortunately).

3)here i got only the formula right, but i don't know how to calculate it correctly: what i got is: #P(X \le 15|X>8) = \frac{P(8 < X \le 15)}{P(X>8)}=\frac{P(8 < X \le 15 | A)P(A)+P(8 < X \le 15 |A^C)P(A^C)}{P(8< X | A)P(A)+P(8< X |A^C)P(A^C)}#

he waiting time in minutes for a bus in a certain station(from getting to the station until the bus arrival) is a random exponential variable with a mean of 10. But if the the traffic is busy, then its mean is 20. The probability that the traffic will be busy when waiting for the bus is 0.18.

1)what is the probability that a man that arrives in random time will wait longer than 15 minutes?

2)if a man waits longer than 15 minutes,what is the probability that the traffic is busy?

3)if a man comes in a random day and after 8 minutes still waiting, what is the probability he'll have to wait for not longer than 15 minutes?

what i already did:

1) expected variance: 14.76, expected mean= 11.8. using z score the result is 0.2.

2)defined the events a - being late, b−x>15.p(a)=0.2,

3)here i got only the formula right, but i don't know how to calculate it correctly: what i got is:

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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