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2 years ago

Can anyone please help me with this question? Soon as possible.

Mathematics

1 answer:

olga_2 [115]2 years ago

8 0

I think the answer is y=-2(x-2)^2+6

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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:

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

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3 years ago

You are watching a commercial on television for the newest sandwich at ur favorite fast food chain.what type of promotion are u

zheka24 [161]

You are watching an advertisement

4 0

3 years ago

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Find the area of a parallelogram with sides 6 and 12 and an angle of 60

KiRa [710]

Hello,

Let's assume h the heigth of the parallelogram

h/6=sin 60°==>h=√3/2*6=3√3
Area=3√3 * 12=36√3

8 0

3 years ago

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What is 1/3 out of 100%

Andrej [43]

The answer your looking for is 33.3%

(it goes on a lot longer but that's just rounded to 1 decimal place)

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3 years ago

Help with this problem pleaseeee

RUDIKE [14]

Step-by-step explanation:

(16 ×7×3)+(1/2×3×5×6)

=336+45

=381cubic inch

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3 years ago