Answer:
a) For this case we define the random variable as X ="waiting time during peak hours" and we know that this distribution follows an uniform distribution:
![X \sim Unif(a=0,b=8)](https://tex.z-dn.net/?f=%20X%20%5Csim%20Unif%28a%3D0%2Cb%3D8%29)
Where a and b represent the limits of the distribution.
b) ![f(x) = \frac{1}{8}= 0.125, a\leq x \leq b](https://tex.z-dn.net/?f=%20f%28x%29%20%3D%20%5Cfrac%7B1%7D%7B8%7D%3D%200.125%2C%20a%5Cleq%20x%20%5Cleq%20b)
And the height for this case would be 0.125
Step-by-step explanation:
Part a
For this case we define the random variable as X ="waiting time during peak hours" and we know that this distribution follows an uniform distribution:
![X \sim Unif(a=0,b=8)](https://tex.z-dn.net/?f=%20X%20%5Csim%20Unif%28a%3D0%2Cb%3D8%29)
Where a and b represent the limits of the distribution.
Part b
For this case the density function would be given by:
![f(x) = \frac{1}{8}= 0.125, a\leq x \leq b](https://tex.z-dn.net/?f=%20f%28x%29%20%3D%20%5Cfrac%7B1%7D%7B8%7D%3D%200.125%2C%20a%5Cleq%20x%20%5Cleq%20b)
And the height for this case would be 0.125
And
for other case.
The cumulative distribution function would be given by:
![F(x) = 0, x](https://tex.z-dn.net/?f=%20F%28x%29%20%3D%200%2C%20x%3C0)
![F(x) = \frac{x-a}{b-a}= \frac{x}{8}, 0\leq x < 8](https://tex.z-dn.net/?f=%20F%28x%29%20%3D%20%5Cfrac%7Bx-a%7D%7Bb-a%7D%3D%20%5Cfrac%7Bx%7D%7B8%7D%2C%200%5Cleq%20x%20%3C%208)
![F(x) = 1, x\geq 8](https://tex.z-dn.net/?f=%20F%28x%29%20%3D%201%2C%20x%5Cgeq%208)