What is the formula for the expected number of successes in a binomial experiment with n trials and probability of success p? C
hoose the correct forumla below.
A. Upper E (Upper X )equalsStartRoot np (1 minus p )EndRoot
B. Upper E (Upper X )equalsp Superscript n
C. Upper E (Upper X )equals (1 minus p )Superscript n(1 minus p )Superscript n
D. Upper E (Upper X )equalsnp
1 answer:
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.)
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Answer:
i think A
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AAS
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Hello there!
The correct answer is option C
3x + 20x - 55 = -9
I am not sure if you wanted some more details but I hope this helps and if you do, just let me and I will edit it.
Good luck with your studies!
Happy New Year!~
Answer:
I dont know.. sorry.......
Answer:
first find the area of the big rectangle = 12×14=168
area of the small unshaded rectangle =2×5×6=60
area of the shaded region = 168-60=108