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3 years ago

How can you use a number line to find the sum of -4 and positive 6

Mathematics

1 answer:

MrRissso [65]3 years ago

3 0

Start at -4 and go over to the right 6. - is left and +is right. the answer is 2.

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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

Need help please and Thank you

Novosadov [1.4K]

Top left:
7x-44 = 4x+4
7x-4x = 4+44
3x = 48
x = 16
8y-43 = 39+(7(16)-44)
8y = 39+68+43
8y = 150
y = 18.75

7 0

3 years ago

Answer this math quedtion <br> 40s+(2b)s+200

Elina [12.6K]

Is it supposed to be equal to something, maybe "0"? You wouldn't be able to solve this without that.

5 0

3 years ago

Volume of a triangular prism

Strike441 [17]

The formula is the area of the base times the height.<span>

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6 0

3 years ago

Read 2 more answers

what proteins embedded in the phospholipid bilayer do what in the cell membrane? A) organize amino acids for protein synthesis B

ohaa [14]

Answer: The answer is (D) prevent the passge of certian molecules into the cell.

Step-by-step explanation: We have four option out of which one describes the functions of protein present in the phospholipid bilayer in the cell membrane.

Phospholipid bilayers are critical components of cell membranes. Its function is to act as a barrier to the passage of molecules and ions into and out of the cell. It allows selective substances and molecules to come in and go out of the membrane.

Thus, the correct option is (D).

8 0

3 years ago