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3 years ago

Need some help please

Mathematics

1 answer:

Anon25 [30]3 years ago

4 0

Answer:

3 cups

Step-by-step explanation:

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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:

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

5 0

3 years ago

A giant scoop, operated by a crane, is in the shape of a hemisphere of radius 21 inches. The scoop is used to transfer molten st

eduard

Answer:

31.5 in

Step-by-step explanation:

Volume of a hemisphere = (2/3) $\pi$ r³
(where r is the radius)
Volume of a cylinder = $\pi$ r²h
(where r is the radius and h is the height)
radius r = (1/2) diameter

First, find the volume of the scoop using the volume of a hemisphere formula with r = 21:

Volume = (2/3) $\pi$ x 21³ = 6174 $\pi$ in³

Now equate the found volume of the scoop to the equation of the volume of a cylinder with r = 14, and solve for h:

$\pi$ 14²h = 6174 $\pi$

196 $\pi$ h = 6174 $\pi$

Divide both sides by $\pi$ : 196h = 6174

Divide both sides by 196: h = 31.5

Therefore, the height of the molten steel in the storage tank is 31.5 in

3 0

2 years ago

Find the missing factor. 200 x ____ = 600 A) 2 B) 3 C) 4 D) 5

kykrilka [37]

Answer:

B. 3

Step-by-step explanation:

we know 2x3 = 6 soo just add 2 zeros = 600

4 0

2 years ago

Read 2 more answers

If 2 miles is equal to 3,218.7meters, how many meters are there in 7 miles

AysviL [449]

3218.7/2 is 1 mile so answer is
2(3218.7/2)= 11265.45

7 0

2 years ago

Sammy bought 3 T-shirts for $15.75 each and pairs of jeans for $28.79 each. If the sales tax on his purchases totaled $5.24, how

abruzzese [7]

Answer: $49.78

Step-by-step explanation: $15.75 + $28.79 + $5.24 = $49.78

7 0

3 years ago

Need some help please ​

Need some help please