Translation will be your answer, for it just moved, but didn't change
hope this helps
The transformation of this shape was rotation, it was rotated 180 degrees clockwise around the axis.
I think it might be B sorry
Answer:
a
![P(X = 0) = 0.6065](https://tex.z-dn.net/?f=%20P%28X%20%3D%200%29%20%3D%20%200.6065%20)
b
![P(x < 25 ) = 1.18 *10^{-33}](https://tex.z-dn.net/?f=P%28x%20%3C%20%2025%20%29%20%3D%20%20%201.18%20%2A10%5E%7B-33%7D%20)
c
Step-by-step explanation:
From the question we are told that
The rate is
= 0.5 / hr
Generally Poisson distribution formula is mathematically represented as
![P(X = x) = \frac{(\lambda t) ^x e^{-\lambda t }}{x!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%20%5Cfrac%7B%28%5Clambda%20t%29%20%5Ex%20e%5E%7B-%5Clambda%20t%20%7D%7D%7Bx%21%7D)
Generally the probability that no error occurred during a day is mathematically represented as
Here t = 1 hour according to question a
So
![P(X = x) = \frac{\lambda^x e^{-\lambda}}{x!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%20%5Cfrac%7B%5Clambda%5Ex%20e%5E%7B-%5Clambda%7D%7D%7Bx%21%7D)
Hence
![[tex]P(X = 0) = \frac{\frac{1}{2} ^0 e^{-\frac{1}{2}}}{0!}](https://tex.z-dn.net/?f=%5Btex%5DP%28X%20%3D%200%29%20%3D%20%20%5Cfrac%7B%5Cfrac%7B1%7D%7B2%7D%20%5E0%20e%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%7D%7B0%21%7D)
=> ![P(X = 0) = 0.6065](https://tex.z-dn.net/?f=%20P%28X%20%3D%200%29%20%3D%20%200.6065%20)
Generally the probability that a critical error occurs since the start of a day is mathematically represented as
Here t = 1 hour according to question a
So
![P(X = x) = \frac{\lambda^x e^{-\lambda}}{x!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%20%5Cfrac%7B%5Clambda%5Ex%20e%5E%7B-%5Clambda%7D%7D%7Bx%21%7D)
Hence
![P(x \ge 25 ) = 1 - P(x < 25 )](https://tex.z-dn.net/?f=P%28x%20%5Cge%2025%20%29%20%3D%20%201%20-%20P%28x%20%3C%20%2025%20%29)
Here
![P(x < 25 ) = \sum_{x=0}^{24} \frac{e^{-\lambda} * \lambda^{x}}{x!}](https://tex.z-dn.net/?f=P%28x%20%3C%20%2025%20%29%20%3D%20%5Csum_%7Bx%3D0%7D%5E%7B24%7D%20%5Cfrac%7Be%5E%7B-%5Clambda%7D%20%2A%20%5Clambda%5E%7Bx%7D%7D%7Bx%21%7D)
=> ![P(x < 25 ) = \frac{e^{-0.5} *0.5^{0}}{0!} + \cdots + \frac{e^{-0.5} *0.5^{24}}{24!}](https://tex.z-dn.net/?f=P%28x%20%3C%20%2025%20%29%20%3D%20%20%5Cfrac%7Be%5E%7B-0.5%7D%20%2A0.5%5E%7B0%7D%7D%7B0%21%7D%20%2B%20%5Ccdots%20%2B%20%5Cfrac%7Be%5E%7B-0.5%7D%20%2A0.5%5E%7B24%7D%7D%7B24%21%7D)
![P(x < 25 ) = 0.6065 + \cdots + \frac{e^{-0.5} *0.5^{24}}{6.204484 * 10^{23}}](https://tex.z-dn.net/?f=P%28x%20%3C%20%2025%20%29%20%3D%20%200.6065%20%2B%20%5Ccdots%20%2B%20%5Cfrac%7Be%5E%7B-0.5%7D%20%2A0.5%5E%7B24%7D%7D%7B6.204484%20%2A%2010%5E%7B23%7D%7D)
![P(x < 25 ) = 0.6065 + \cdots + 6.0*10^{-32}](https://tex.z-dn.net/?f=P%28x%20%3C%20%2025%20%29%20%3D%20%200.6065%20%2B%20%5Ccdots%20%2B%206.0%2A10%5E%7B-32%7D)
![P(x < 25 ) = 1.18 *10^{-33}](https://tex.z-dn.net/?f=P%28x%20%3C%20%2025%20%29%20%3D%20%20%201.18%20%2A10%5E%7B-33%7D%20)
Considering question c
Here t = 2
Gnerally given that the system just started up and an error occurred the probability the next reset will occur within 2 hours
![P(x \le 5 ) = \sum_{n=0}^{5} \frac{(\lambda t) ^x e^{-\lambda t }}{x!}](https://tex.z-dn.net/?f=P%28x%20%5Cle%205%20%29%20%3D%20%20%5Csum_%7Bn%3D0%7D%5E%7B5%7D%20%20%5Cfrac%7B%28%5Clambda%20t%29%20%5Ex%20e%5E%7B-%5Clambda%20t%20%7D%7D%7Bx%21%7D)
=> ![P(x \le 5 ) = \frac{(0.5 * 2) ^ 0 e^{- 0.5 * 2 }}{0!} + \cdots + \frac{(0.5 * 2) ^ 5 e^{- 0.5 * 2 }}{5!}](https://tex.z-dn.net/?f=P%28x%20%5Cle%205%20%29%20%3D%20%20%20%5Cfrac%7B%280.5%20%2A%20%202%29%20%5E%200%20e%5E%7B-%200.5%20%20%2A%202%20%7D%7D%7B0%21%7D%20%2B%20%5Ccdots%20%20%2B%20%20%20%5Cfrac%7B%280.5%20%2A%20%202%29%20%5E%205%20%20e%5E%7B-%200.5%20%20%2A%202%20%7D%7D%7B5%21%7D)
=> ![P(x \le 5 ) = \frac{1* 2.7183 }{1 } + \cdots + \frac{1 *2.7183 }{120}](https://tex.z-dn.net/?f=P%28x%20%5Cle%205%20%29%20%3D%20%20%20%5Cfrac%7B1%2A%202.7183%20%7D%7B1%20%7D%20%2B%20%5Ccdots%20%20%2B%20%20%20%5Cfrac%7B1%20%20%2A2.7183%20%7D%7B120%7D)
=>