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2 years ago

Please help me out if appreciate it :)

Mathematics

1 answer:

12345 [234]2 years ago

4 0

Answer:

Step-by-step explanation:

they are congruent so they are equal to eachotjer

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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

Suppose a basketball team had a season of games with the following characteristics:

Masteriza [31]

Answer:

Hello Sir/ Mam

YOUR REQUIRED ANSWER IS 18.6%

Variables defined in the question:

H - Home - Games

W - Winning Games

Now, given:

P(H0.62 PW)0.22

P(W\mid H)=0.30

Required : Of all the games, percentage of games that were at home wins.

Hence, required :

P(W\cap H)

Now, we know that:

P(W\mid H)=\frac{P(W\cap H)}{P(H)}

0.3=\frac{P(W\cap H)}{0.62}

Hence,

P(W\cap H)=0.3*0.62=0.186=18.6\%

I hope this solves your doubt.

Feel free to comment if you still have any query.

Do give a thumbs up if you find this helpful.

Step-by-step explanation:

5 0

3 years ago

The line for the equation y = 1 horizontal or vertical? What is the slope of this line?

Nimfa-mama [501]

Answer:

The line is horizontal and the slope is 0.

Step-by-step explanation:

Any line that is horizontal has a slope of 0.

7 0

3 years ago

What is the value of the growth factor of the function? A) 1/5 B) 1/3 C) 2 D) 6

ICE Princess25 [194]

Answer:

Step-by-step explanation:

Divide 18 by one third and see what ya get

then 6, then 2. BOOM!

7 0

3 years ago

Mike pays $20 per hour for algebra tutoring. The equation y = 20x relates the cost of tutoring (y) to the number of hours (x) he

kotykmax [81]

The unit rate in the equation is 20.

Option C) is the correct answer.

Step-by-step explanation:

Step 1 :

In the given equation y = 20x

where,

x ⇒ total number of hours for tutoring

20 ⇒ the cost per hour of tutoring

y ⇒ the total cost for total hours of tutoring

Step 2 :

Unit rate refers to the value per hour.

Here, the cost for 1 hour of tutoring is $20.

∴ The unit rate is $20 per hour of tutoring.

8 0

4 years ago