Answer:
![(D)E[ X ] =np.](https://tex.z-dn.net/?f=%28D%29E%5B%20X%20%5D%20%3Dnp.)
Step-by-step explanation:
Given a binomial experiment with n trials and probability of success p,
Since each term of the summation is multiplied by x, the value of the term corresponding to x = 0 will be 0. Therefore the expected value becomes:
Now,
Substituting,
Factoring out the n and one p from the above expression:
Representing k=x-1 in the above gives us:
This can then be written by the Binomial Formula as:
![E[ X ] = (np) (p +(1 - p))^{n -1 }= np.](https://tex.z-dn.net/?f=E%5B%20X%20%5D%20%3D%20%28np%29%20%28p%20%2B%281%20-%20p%29%29%5E%7Bn%20-1%20%7D%3D%20np.)
The simplified polynomial that represents how many more economy cars are rented in w weeks than full-size cars is 53 - w.
<h3>Linear equation:</h3>
Linear equation is an equation in which the highest power of the variable is equals to one.
Therefore, the number of economy-size cars rented in w weeks is represented as follows:
The number of full-size cars rented in w weeks is represented as follows:
where
w = number of weeks
A simplified polynomial that represents how many more economy cars are rented in w weeks than full-size cars is as follows:
- 152 + 3w - (99 + 2w)
- 152 + 3w - 99 - 2w
- 53 - w
learn more on polynomial here: brainly.com/question/2566362
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