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3 years ago

Help me out hereeeeeeeeee

Mathematics

2 answers:

Alja [10]3 years ago

4 0

Answer:

the second answer

Step-by-step explanation:

I hope it helps

frutty [35]3 years ago

4 0

Answer:

1 5/8

Step-by-step explanation:

5/8 * 3 = 15/8 which is the same as 1 7/8

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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

Problem: -7(2)+y=60, so where do I start?

aev [14]

-7(2)+y=60
-14+y=60
y=60+14
Y=74

4 0

3 years ago

Read 2 more answers

Jordan Pat 6 4/5 yards of pink ribbon and 3 1/4 yards of purple ribbon how much more pink ribbon the purple ribbon did she buy?

evablogger [386]

Hello! For this question, we will have to subtract fractions. In order to do this, we will have to convert the fractions into the same denominator. We do this by finding the LCD of the two numbers. In other words, we find the LCM. The LCM of 5 and 4 is 20. 4/5 converts to 16/20, and 1/4 converts to 5/20. Let's subtract these numbers like we would regular numbers. 6 16/20 - 3 5/20 is 3 11/20. There. Jordan bought 3 11/20 yards more pink ribbon than purple ribbon.

8 0

3 years ago

Help ASAP please! Thank you so much<br> What is the slope of the graphed line?

galina1969 [7]

Answer:

the numbers aren't clear can you enlarge the screenshot?

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

How many segments of length x will fit into the circumference of this circle? Express your answer to the nearest hundredth.

Trava [24]

Answer:

<h2><u><em>the circumference of a circle is defined as:</em></u></h2><h2><u><em></em></u></h2><h2><u><em>c = pi*diameter</em></u></h2><h2><u><em></em></u></h2><h2><u><em>if we have x segments of length y, then we can fit:</em></u></h2><h2><u><em></em></u></h2><h2><u><em>c/y = z</em></u></h2><h2><u><em></em></u></h2><h2><u><em>we can fit z segments of size y on the circumference c</em></u></h2><h2><u><em></em></u></h2>

6 0

2 years ago