HELP ME PLEASE!!! Please

What is the formula for the expected number of successes in a binomial experiment with n trials and probability of success p? C

charle [14.2K]

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:

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

5 0

3 years ago

I need help with this?

Dmitrij [34]

el triangulo que forma el radio es un triangulo equilátero y por lo tanto el lado del hexágono sera de la misma medida que el radio:

lado = radio = 2 cm

como hay 6 lados, lo multiplicamos por 6 :

2x6 = 12 cm

entonces el perímetro del hexágono es 12 cm

Saludos¡

6 0

2 years ago

Read 2 more answers

How many solutions does the following equation have? 10x-1=10x+4

zimovet [89]

Your answer is no solution.
Because if we transpose 10x to the left hand side with a change in the symbol, then it will become 0.
10x - 1 = 10x +4
or, 10x - 10x = 4 + 5
or, 0 = 9
Hence, the equation has <em><u>no solution</u></em>.

Hope you could get an idea from here.

Doubt clarification - use comment section.

7 0

2 years ago

Read 2 more answers

PLEEEEEEEEEEASSEEEEEEE ANSWER QUESTION IS DOWN BELOW WORTH 15 POINTS each

Svetllana [295]

A ratio shows us the number of times a number contains another number. The ratio of the volume of the model to the volume of the original is 27/2744.

<h3>What is a Ratio?</h3>

A ratio shows us the number of times a number contains another number.

Given that the scale factor is 3:14. Therefore, the ratios can be written as,

(a) The ratio of the surface area of the model to the surface area of the original is,

Surface area Ratio = (3/14)² = 9/196

(b) The ratio of the volume of the model to the volume of the original.

Volume Ratio = (3/14)³ = 27/2744

(c) The ratio of the width of the model to the width of the original.

Width Ratio = 3/14

Learn more about Ratios:

brainly.com/question/1504221

#SPJ1

3 0

2 years ago

Select the correct answer<br> What are the zeros of the graphed function?

VashaNatasha [74]

Answer:

○ C. $\displaystyle 0, 2, and\:4$

Step-by-step explanation:

Wherever the graph intersects the x-axis is considered your zero [x-intercept], therefore you have your answer:

$\displaystyle [0, 0], [2, 0], and\: [4, 0]$

I am joyous to assist you at any time.

8 0

2 years ago