D. 2x2+3x-x2+y+y-(x2+2y)=3

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 canoe in still water travels at a rate of 12 miles per hour. The current today is traveling at a rate of 2 miles per hour. If

VARVARA [1.3K]

Answer:

It’s 60miles

Step-by-step explanation:

We assume the trip is "d" miles and that the "extra hour" refers to the additional time that a current of 2 mph would add. That is, we assume the reference time is for a current of 0 mph.

The time with no current is ...

time1 = distance/speed

time1 = d/12 . . . . hours

With a current of 2 mph in the opposite direction, the time is ...

time2 = d/(12 -2) = d/10

The second time is 1 hour longer than the first, so we have ...

time2 = 1 + time1

d/10 = 1 + d/12

6d = 60 + 5d . . . . multiply by 60

d = 60 . . . . . . . . . subtract 5d

The one-way distance is 60 miles.

7 0

2 years ago

Simplify the given expression. (18+ - 8)2

JulsSmile [24]

Answer:

20

Step-by-step explanation:

Our expression:

2 * (18 + - 8)

Plus then minus (+ -) is the same as just minus ( - )

Some examples:

1 + (+ 1) = 2

1 + (- 1) = 0

1 - (+ 1) = 0

1 - (- 1) = 2

Thus, 18 + - 8 is the same as 18 - 8

2 * (18 + - 8) =

= 2 * (18 - 8) =

= 2* (10) =

= 2 * 10 =

= 20

Answer: 20

6 0

2 years ago

What is -5/4 minus 7?

DaniilM [7]

Answer:

-33/4 or -8 1/4

Step-by-step explanation:

Make similar terms:

-5/4 - 28/4: then solve

-5 - 28 = -33: put over 4

-33/4: simplify

-8 1/4

7 0

3 years ago

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What is the value of x?

BlackZzzverrR [31]

We can use the Pythagorean theorum

a^2+b^2=c^2

c^2 is the length of the longest side squared

so

6^2 + b^2 = 10^2

36+ b^2 = 100
-36 -36

b^2 = 64

b = 8

b is the same thing as your "x", so x = 8

7 0

2 years ago

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