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.)
Answer:
about a half teaspoon
Step-by-step explanation:
Answer:
18
Step-by-step explanation:



Answer:
-499,485.
Step-by-step explanation:
We can transform this to an arithmetic series by working it out in pairs:
6^2 - 7^2 = (6-7)(6+7) = -13
8^2 - 9^2 = (8-9)*8+9) = -17
10^2 - 11^2 = -1 * 21 = -21 and so on
The common difference is -4.
The number of terms in this series is (998 - 6) / 2 + 1
= 992/2 + 1 = 497.
Sum of n terms of an A.S:
= n/2 [2a1 + (n - 1)d
Here a1 = -13, n = 497, d = -4:
Sum = (497/2)[-26 - 4(497-1)]
= 497/2 * -2010
= -499,485.