X=6 if you need an explanation commu
Answer:
(a) The probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function is 0.7981.
(b) The probability of waiting less than 12 minutes between successive speeders using the probability density function is 0.7981.
Step-by-step explanation:
The cumulative distribution function of the random variable <em>X, </em>the waiting time, in hours, between successive speeders spotted by a radar unit is:

(a)
Compute the probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function as follows:

The probability is:


Thus, the probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function is 0.7981.
(b)
The probability density function of <em>X</em> is:

Compute the probability of waiting less than 12 minutes between successive speeders using the probability density function as follows:

![=8\times [\frac{-e^{-8x}}{8}]^{0.20}_{0}\\\\=[-e^{-8x}]^{0.20}_{0}\\\\=(-e^{-8\times 0.20})-(-e^{-8\times 0})\\\\=-0.2019+1\\\\=0.7981](https://tex.z-dn.net/?f=%3D8%5Ctimes%20%5B%5Cfrac%7B-e%5E%7B-8x%7D%7D%7B8%7D%5D%5E%7B0.20%7D_%7B0%7D%5C%5C%5C%5C%3D%5B-e%5E%7B-8x%7D%5D%5E%7B0.20%7D_%7B0%7D%5C%5C%5C%5C%3D%28-e%5E%7B-8%5Ctimes%200.20%7D%29-%28-e%5E%7B-8%5Ctimes%200%7D%29%5C%5C%5C%5C%3D-0.2019%2B1%5C%5C%5C%5C%3D0.7981)
Thus, the probability of waiting less than 12 minutes between successive speeders using the probability density function is 0.7981.
The correct answer is Choice A.
This is an example of an exponential equation, so we need the formula

.
The a value is the starting value of 100. The b value must be a decimal lower than 1 because it is decreases.
If you substitute in 8 for x, you will see that the output is about 50 (half of 100).
Slope = (-7-8)/(3+4) = -15/7
We cannot determine the y-intercept unless we know at least 2 points.
Pls thank me if i am right
I hope this helped:D