1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
STatiana [176]
3 years ago
7

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
Mathematics
1 answer:
charle [14.2K]3 years ago
5 0

Answer:

(D)E[ X ] =np.

Step-by-step explanation:

Given a binomial experiment with n trials and probability of success​ p,

f(x)=\left(\begin{array}{c}n\\k\end{array}\right)p^x(1-p)^{n-x}, 0\leq  x\leq n

E(X)=\sum_{x=0}^{n}xf(x)= \sum_{x=0}^{n}x\left(\begin{array}{c}n\\k\end{array}\right)p^x(1-p)^{n-x}

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:

E(X)=\sum_{x=1}^{n}x\left(\begin{array}{c}n\\x\end{array}\right)p^x(1-p)^{n-x}

Now,

x\left(\begin{array}{c}n\\x\end{array}\right)= \frac{xn!}{x!(n-x)!}=\frac{n!}{(x-)!(n-x)!}=\frac{n(n-1)!}{(x-1)!((n-1)-(x-1))!}=n\left(\begin{array}{c}n-1\\x-1\end{array}\right)

Substituting,

E(X)=\sum_{x=1}^{n}n\left(\begin{array}{c}n-1\\x-1\end{array}\right)p^x(1-p)^{n-x}

Factoring out the n and one p from the above expression:

E(X)=np\sum_{x=1}^{n}n\left(\begin{array}{c}n-1\\x-1\end{array}\right)p^{x-1}(1-p)^{(n-1)-(x-1)}

Representing k=x-1 in the above gives us:

E(X)=np\sum_{k=0}^{n}n\left(\begin{array}{c}n-1\\k\end{array}\right)p^{k}(1-p)^{(n-1)-k}

This can then be written by the Binomial Formula as:

E[ X ] = (np) (p +(1 - p))^{n -1 }= np.

You might be interested in
Draw a line representing the "rise " and a line representing the "run" of the line. State the slope of the line in simplest form
murzikaleks [220]

Answer:

4/5

Step-by-step explanation:

you rise up from the line where it is exactly going throw another line. (like it would make a point) fine another time where it happens and rise count up or down and count up and run count left or right. then you'll have a fraction

7 0
2 years ago
What is 89,659 rounded to the nearest hundred thousand
Novay_Z [31]
89.659 \to \boxed{90.000}
7 0
3 years ago
Read 2 more answers
What is the product of one half and two thirds?
attashe74 [19]

Answer:

1/4

Step-by-step explanation:

1/2 × 2/3

= 1×3 = 1

2×2 = 4

Therefore,

1/2 × 2/3 = 1/4//

4 0
3 years ago
Math question || thank uu
lesya [120]

Answer:

Step-by-step explanation:

plot an open circle on the 4 and a closed circle on the 10. Then draw a line that goes from 4 to 10.

4 0
2 years ago
What is the greatest common factor of 52x5 and 12x4
Pani-rosa [81]
"A. 4x^4 is the answer so try that."
7 0
3 years ago
Read 2 more answers
Other questions:
  • Who is traditionally seen as the inventor of linear perspective?
    10·1 answer
  • Billy is 3 feet 6 inches tall. Billy’s stuffed bear is 14 inches tall. What is the ratio of Billy’s height to the height of his
    7·2 answers
  • Please answer this question
    12·2 answers
  • Find the missing measures for the rectangle. l = _?_ w = 4.2 m A = 37.8 m2 P = _?_ A) 9 m; 26.4 m B) 14.7 m; 61.74 m C) 9 m; 13.
    5·1 answer
  • (Based on Q1 ~ Q3) According to the Bureau of the Census, 18.1% of the U.S. population lives in the Northeast, 21.9% inn the Mid
    5·1 answer
  • I am struggling hard out with linear algebra in math level one
    13·1 answer
  • A baseball team is in second place with a win to loss ratio of .535. What percent of the games played did the team win?
    9·2 answers
  • Consider the equation y\:=\:-x^2\:-\:7x\:+\:12. Determine whether the function has a maximum or a minimum value. State the maxim
    6·1 answer
  • If f(x) = 3x + 4(x + 1) + 2 then f (4x) =?
    10·2 answers
  • Help please i dont know the answer
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!