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mrs_skeptik [129]

3 years ago

12

How does knowing multiplication rules help solve problems faster and easier

2 answers:

Ivenika [448]3 years ago

8 0

I was about to say what the person said

KengaRu [80]3 years ago

3 0

Answer: It helps because you already know it off the top of your head and you are able to break up a multiplication problem step by step in your head.

Step-by-step explanation:

You might be interested in

there are 12 actors auditioning for 5 different roles in a new play. how many different cast are possible

aleksandr82 [10.1K]

Answer:

95,040 different cast are possible

Step-by-step explanation:

In this case the order in which the actors are selected for the 5 different roles is important. Therefore we use the permutations formula.

$nPr =\frac{n!}{(n-r)!}$

Where n is the number of items you can choose and choose r from them.

In this case $n = 12$ and $r = 5$

$12P5 =\frac{12!}{(12-5)!}$

$12P5 =\frac{12!}{7!}$

$12P5 =95040$

3 0

3 years ago

I need some help with this

bonufazy [111]

1st blank: 2x
2nd blank: 4x
3rd blank: 8
4th blank: 16
5th blank: 4

4 0

3 years ago

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

Solve the equation. –3x + 9 = –3(2x + 3) + 3(x – 4) + 1 How many solutions does this equation have? one solution two solutions i

gavmur [86]

-3x+9 = -3(2x+3) + 3(x-4)+1

distribute

-3x+9 =-6x-9+3x-12+1

add like terms

-3x+9= -3x-20

add 3x to each side

9 = -20

there are no solutions because 9 does not equal -20

6 0

2 years ago

Read 2 more answers

What is the relative change from 6546 to 4392

vlada-n [284]

Answer:

The relative change from 6546 and 4392 is 49.04

Step-by-step explanation:

4 0

3 years ago