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Rudiy27
3 years ago
11

Find y when x=15 if y=6 when x=30

Mathematics
1 answer:
Elan Coil [88]3 years ago
6 0

Answer:


Step-by-step explanation:

the answer would be nine

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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
If you add 15 calls and multiple them by the total of 67 keeps and there is only one 1 Jeep subtract that by 56 and add 100 divi
yan [13]

Answer:

IT would give you a decimal whis is 966.66666666667

Step-by-step explanation:

15*67+1-56+100/6

4 0
2 years ago
Read 2 more answers
What data type (string, integer, float) you would expect the terminal to return?
vazorg [7]
I’m sorry what subject is this I will still help u
5 0
3 years ago
What is the image of the point (3, -2) under a dialtion with a scale factor of 4 with respect to the origin?
Bogdan [553]

Answer:

(12,-8)

Step-by-step explanation:

scale factor is 4

(x,y)=(4x,4y)

(3,-2)=(12,-8)

3 0
3 years ago
Patti's Pet Palace has a 90-gallon fish tank. When it needs to be cleaned, it can be drained at a rate of 2 gallons per minute.
dangina [55]
Y = 90 - 2x

This should be the correct answer
6 0
3 years ago
Read 2 more answers
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