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2 years ago

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Angle 1 and 2 are same side interior angles formed by two parallel lines and a transversal. If measure of angle 1 is 115, what i

s measure of angle 2

1 answer:

dalvyx [7]2 years ago

4 0

Same side interior angles = 180.

180-115 =65

Angle 2 = 65

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

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2 years ago

Kayla drives 15 miles in 20 minutes. If she drove one hour in total at the same rat how far did she go? Before you try that prob

alisha [4.7K]

Answer:

Kayla drove 45miles

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The formula for finding the area of a square that has a side length, s, is A = s^2. If a square has an area of 40 square units,

Darina [25.2K]

A = s^2
A = 40

40 = s^2...by taking the square root of both sides, u eliminate the ^2
sqrt 40 = s
6.32 = s <===

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2 years ago

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Does doubling the radius of a sphere double the surface area? Explain your reasoning using an example.

Annette [7]

Answer:

yes

Step-by-step explanation:

because area of sphere equals =

$4\pi \: r{2}$

so if we doubled the radius the surface area will be doubled

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2 years ago

Shelby charges $12 an hour for lawn care. Over the summer, he earne

asambeis [7]

Answer:

Don't be lazy, do it by yourself for more brain work!

Step-by-step explanation:

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1 year ago