Answer:
The distribution is ![\frac{\lambda^{n}e^{- \lambda t}t^{n - 1}}{(n - 1)!}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Clambda%5E%7Bn%7De%5E%7B-%20%5Clambda%20t%7Dt%5E%7Bn%20-%201%7D%7D%7B%28n%20-%201%29%21%7D)
Solution:
As per the question:
Total no. of riders = n
Now, suppose the
is the time between the departure of the rider i - 1 and i from the cable car.
where
= independent exponential random variable whose rate is ![\lambda](https://tex.z-dn.net/?f=%5Clambda)
The general form is given by:
![T_{i} = \lambda e^{- lambda}](https://tex.z-dn.net/?f=T_%7Bi%7D%20%3D%20%5Clambda%20e%5E%7B-%20lambda%7D)
(a) Now, the time distribution of the last rider is given as the sum total of the time of each rider:
![S_{n} = T_{1} + T_{2} + ........ + T_{n}](https://tex.z-dn.net/?f=S_%7Bn%7D%20%3D%20T_%7B1%7D%20%2B%20T_%7B2%7D%20%2B%20........%20%2B%20T_%7Bn%7D)
![S_{n} = \sum_{i}^{n} T_{n}](https://tex.z-dn.net/?f=S_%7Bn%7D%20%3D%20%5Csum_%7Bi%7D%5E%7Bn%7D%20T_%7Bn%7D)
Now, the sum of the exponential random variable with
with rate
is given by:
![S_{n} = f(t:n, \lamda) = \frac{\lambda^{n}e^{- \lambda t}t^{n - 1}}{(n - 1)!}](https://tex.z-dn.net/?f=S_%7Bn%7D%20%3D%20f%28t%3An%2C%20%5Clamda%29%20%3D%20%5Cfrac%7B%5Clambda%5E%7Bn%7De%5E%7B-%20%5Clambda%20t%7Dt%5E%7Bn%20-%201%7D%7D%7B%28n%20-%201%29%21%7D)
Answer:
-84
Step-by-step explanation:
Answer:
The sum of the digit of the product is 13
Step-by-step explanation:
Given
![2*5*7*2*5*7*2*5](https://tex.z-dn.net/?f=2%2A5%2A7%2A2%2A5%2A7%2A2%2A5)
Solving (a): The product
![Product=2*5*7*2*5*7*2*5](https://tex.z-dn.net/?f=Product%3D2%2A5%2A7%2A2%2A5%2A7%2A2%2A5)
![Product=49000](https://tex.z-dn.net/?f=Product%3D49000)
Solving (b): The sum of the digits
![Sum = 4 + 9 +0 +0+0](https://tex.z-dn.net/?f=Sum%20%3D%204%20%2B%209%20%2B0%20%2B0%2B0)
![Sum = 13](https://tex.z-dn.net/?f=Sum%20%3D%2013)