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2 years ago

Given the midpoint and one endpoint find the other endpoint. Endpoint (2,-9) Midpoint (-2,-1)

Mathematics

1 answer:

AfilCa [17]2 years ago

6 0

Answer:

Step-by-step explanation:

(x + 2)/2 = -2

x + 2 = -4

x = -6

(y + (-9))/2 = -1

y - 9 = -2

y = 7

(-6, 7)

answer is C

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5.2.14. For the negative binomial pdf p (k; p, r) = k+r−1 (1 − p)kpr, find the maximum likelihood k estimator for p if r is know

Volgvan

Answer:

$\hat p = \frac{r}{\bar x +r}$

Step-by-step explanation:

A negative binomial random variable "is the number X of repeated trials to produce r successes in a negative binomial experiment. The probability distribution of a negative binomial random variable is called a negative binomial distribution, this distribution is known as the Pascal distribution".

And the probability mass function is given by:

$P(X=x) = (x+r-1 C k)p^r (1-p)^{x}$

Where r represent the number successes after the k failures and p is the probability of a success on any given trial.

Solution to the problem

For this case the likehoof function is given by:

$L(\theta , x_i) = \prod_{i=1}^n f(\theta ,x_i)$

If we replace the mass function we got:

$L(p, x_i) = \prod_{i=1}^n (x_i +r-1 C k) p^r (1-p)^{x_i}$

When we take the derivate of the likehood function we got:

$l(p,x_i) = \sum_{i=1}^n [log (x_i +r-1 C k) + r log(p) + x_i log(1-p)]$

And in order to estimate the likehood estimator for p we need to take the derivate from the last expression and we got:

$\frac{dl(p,x_i)}{dp} = \sum_{i=1}^n \frac{r}{p} -\frac{x_i}{1-p}$

And we can separete the sum and we got:

$\frac{dl(p,x_i)}{dp} = \sum_{i=1}^n \frac{r}{p} -\sum_{i=1}^n \frac{x_i}{1-p}$

Now we need to find the critical point setting equal to zero this derivate and we got:

$\frac{dl(p,x_i)}{dp} = \sum_{i=1}^n \frac{r}{p} -\sum_{i=1}^n \frac{x_i}{1-p}=0$

$\sum_{i=1}^n \frac{r}{p} =\sum_{i=1}^n \frac{x_i}{1-p}$

For the left and right part of the expression we just have this using the properties for a sum and taking in count that p is a fixed value:

$\frac{nr}{p}= \frac{\sum_{i=1}^n x_i}{1-p}$

Now we need to solve the value of $\hat p$ from the last equation like this:

$nr(1-p) = p \sum_{i=1}^n x_i$

$nr -nrp =p \sum_{i=1}^n x_i$

$p \sum_{i=1}^n x_i +nrp = nr$

$p[\sum_{i=1}^n x_i +nr]= nr$

And if we solve for $\hat p$ we got:

$\hat p = \frac{nr}{\sum_{i=1}^n x_i +nr}$

And if we divide numerator and denominator by n we got:

$\hat p = \frac{r}{\bar x +r}$

Since $\bar x = \frac{\sum_{i=1}^n x_i}{n}$

4 0

3 years ago

Find f '(a).<br> f(x) = 4x2 − 4x + 3

Vinvika [58]

Use the power rule
d(x^n)/dx = n·x^(n-1)
to form the derivative.
f'(x) = 4·2x -4
f'(x) = 8x - 4

Now, substitute "a" for "x" to find f'(a):
f'(a) = 8a - 4

3 0

3 years ago

A geometric sequence is defined recursively by an=12a(n-1). The first term of the sequence is 0.001. Which of the following is t

Talja [164]

What kind of formula is the answswer supposed to be

6 0

3 years ago

2/21 times 7/8 in simplest form

Angelina_Jolie [31]

2/21 * 7/8

14/168

divide top and bottom by 14

1/12

8 0

2 years ago

1. In Tulsa, Oklahoma the sales tax is 7.9%. If

LenaWriter [7]

Answer:

$ 67.15 tax

Step-by-step explanation:

the tax would be 7.9% of 850

turn ur percent to a decimal....and " of " means multiply

0.079 * 850 = 67.15 <==

3 0

2 years ago