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diamong [38]
3 years ago
15

I will give out BRAINLIEST for the correct answer!

Mathematics
1 answer:
earnstyle [38]3 years ago
8 0

Answer:

2

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
Fabian harvests 10 pounds of tomatoes from his garden. He needs 225 pounds to make a batch of soup. If he sets aside 2.8 pounds
nadya68 [22]
He can make 3 batches of soup.

Starting with 10 pounds of tomatoes and taking out the number of pounds he sets aside for spaghetti sauce, 2.8, we have:
10-2.8 = 7.2 pounds left.

0.2 is read as "two tenths," so 7.2 = 7 2/10

We divide this remaining number of pounds by 2 2/5 for each batch of soup:

7 2/10 ÷ 2 2/5

Convert each to an improper fraction:
72/10 ÷ 12/5

Multiply by the reciprocal:
72/10 × 5/12 = 360/120 = 3


5 0
2 years ago
Please help me i don’t know how to solve this
murzikaleks [220]

Answer:

welp good luck ha

Step-by-step explanation:

3 0
3 years ago
In Sunday's Super Bowl, Tampa Bay ended up winning over Kansas City. With the win, Tampa Bay's Quarterback Tom Brady now has 7 C
Pavlova-9 [17]

Answer:

KANAS CITY CHIEFS ARE THE BEST FRICK TOM BRADY HE IS OLD HE IS 43 YEARS OLD LIKE DUDE STOP UR TO OLD FRICK THE TAMPA BAY BUCS

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Round 3,637 to the nearest thousand
PtichkaEL [24]
Hello There!

It is 4000.

Hope This Helps You!
Good Luck :) 

- Hannah ❤
7 0
2 years ago
Read 2 more answers
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