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3 years ago

I need help in this 10q quiz

Mathematics

2 answers:

slava [35]3 years ago

4 0

Answer:

option A

Step-by-step explanation:

Hope it helps....

soldier1979 [14.2K]3 years ago

3 0

Answer:

Step-by-step explanation:

BY splitting the middle term we get

Y=7x^2+21x+2x+6

Y=7x(x+3)+2(x+3)

y=-3 and -2/7

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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

What is the probability of randomly drawing an odd number between 24 and 33?

Studentka2010 [4]

Write out the numbers between 24 and 33: {24, 25, 26, 27, 28, 29, 30, 31, 32, 33}

How many numbers have we here? 10.

How many of these numbers are odd? {25, 27, 29, 31, 33}

Strictly speaking, "between 24 and 33" does not include {24, 33}.

Thus, the odd numbers between 24 and 33 are {25, 27, 29, 31}

The chances of drawing an odd number between 24 and 33 are then 4 / 10.

If, however, we omit the endpoints 24 and 33, then there are 8 numbers between 24 and 33: {25, 27, 29, 31}

and the odds of choosing an odd number from these eight numbers is 4/8, or 1/2, or 0.50.

6 0

3 years ago

Find the volume of this cylinder. Use 3 for T.

DIA [1.3K]

Answer:

$volume = \pi {r}^{2} h \\ = 3 \times {5}^{2} \times 12 \\ = 900 \: {ft}^{3}$

3 0

3 years ago

What is the range and domain of the graph below?

zavuch27 [327]

Answer:

Domain : All real numbers

Range: x<0

Step-by-step explanation:

6 0

3 years ago

40 pounds of sugar are repackaged of 1/16 pounds each. how many packet of sugar are there?

jarptica [38.1K]

We know to each pound of such, there is 16 packets produced per?

So, 16 x 40 = 640.

8 0

3 years ago

I need help in this 10q quiz ​

I need help in this 10q quiz