The total service time of a multistep manufacturing operation has a gamma distribution with mean 18 minutes and standard deviation 6 minutes.
(a) Determine the parameters alpha and lambda of the distribution. (solving these two parameters using the mean and the standard deviation)
(b) Assume that each step has the same exponential distribution for service time. What distribution for each step and how many steps produce this gamma distribution of total service time?

Answers

Answer 1

Answer:

The answer is "[tex]\bold{r=9, \lambda=\frac{1}{2}\ and \ \ \text{exponential, 9 steps}}[/tex]"

Step-by-step explanation:

In point a:

We are aware of the random gamma variable X:

[tex]\to \mathbb{E} =\frac{r}{\lambda}\\\\\to Std(X) =\frac{\sqrt{r}}{\lambda}\\\\[/tex]

It is given:

[tex]\to \mathbb{E} = 18 \\\\\to std(X)=6[/tex]

[tex]\to 18=\frac{r}{\lambda}\\\\ \to 6=\frac{\sqrt{r}}{\lambda}\\\\[/tex]

Substituting the value:

[tex]\to \frac{\sqrt{r}}{6}=\frac{r}{18}\\\\\to r=9\\\\\to \lambda=\frac{1}{2}\\\\[/tex]

In point b:

When building the Erlang/Gammas distribution, these could reasonably be assumed to become an exponential distribution only with \lambda = 1/2 parameter with one step but to be r = 9 for one step.


Related Questions

help me i am gonna give points to the people give me correct answer

Answers

Answer:

lol

Step-by-step explanation:

Answer:

Arjan should look for other cards that add up to $$94%

Step-by-step explanation:

I don't know it but I guess this one, let me know if it help

A normal six-sided die is thrown once. The number of outcomes in the sample space is

Answers

I think it would be 6 or 1/6

The number of outcomes in the sample space is 6.

What is Probability?

It is a branch of mathematics that deals with the occurrence of a random event.

When you roll a 6 sided dice, number of dots on uppermost face is called as outcome. Now, whenever a dice is rolled we can get either 1, 2,3,4,5 or 6 dots on the upper most face that is now outcome.

So experiment here is "Rolling a 6 faced dice" and list of possible outcomes is "{1,2,3,4,5,6}".

Sample space by its definition is list of all the possible outcomes of an experiment.

S={1,2,3,4,5,6}

Hence, the number of outcomes in the sample space is 6.

To learn more on probability click:

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Angel got 4 problems wrong on a test of 50 questions. What percent of the questions did he get CORRECT

Answers

Answer:

12.5%

Step-by-step explanation:

Answer:

92%

Step-by-step explanation:

50-4 = 46

46/50 *100 = 92%

Write the linear inequality shown in the graph. The gray area represents the shaded region. y ≤ –x + 4 y ≤ –x – 4 y ≥ –x – 4 y ≥ –x + 4

Answers

For Example:

Write the linear inequality shown in the graph. The gray area represents the shaded region.

A. y ≤ 3x + 4

B. y ≤ 3x – 4

C. y ≥ 3x + 4

D. y ≥ 3x – 4

Answer: C

Step-by-step explanation:

1. The graph indicates that the line intersect the y-axis at -4.

2. Then, you must choose any point that are located within the region and replace them to see if the inequality is satisfied. Therefore, you have:

Point (0,2)

I hope this helps! :)

simplify the expression Please HELP

Answers

9 x (24 / 12)^2 + 5

The order of operations is PEMDAS - parenthesis, exponents, multiplication/division, addition/subtraction.

Use the order of operations to know what to simplify first in an expression. P = parenthesis so you simplify what is in parenthesis first. 24/12 = 2, so your first box is 2. The expression now looks like this:
9 x (2)^2 + 5

The next letter is E, which stands for exponents. You square two next. 2^2 = 4 so your next box is 4. The equation now looks like this:

9 x 4 + 5

The next two letters of PEMDAS or MD, which stand for multiplication/division. If you have either or both of these to do in your expression, you do them now. That means you now calculate 9 x 4, which is 36. This leaves you with 36 + 5. Your 3rd box is 36.

The final letters of PEMDAS are AS. Doing any addition/subtraction happens last. Now you can add 36 + 5 to get 41 (your final box)

9 x (24 / 12)^2 + 5 = 41

Let me know if you have any questions/didn’t understand something. I hope this helps :)


Very much need some help ASAP !!

Answers

Answer:

D

Step-by-step explanation:

It cannot be Option A because the values are halve and there is nothing to distribute to them to make the values equal.

It's not option C because if you distribute 2y to each term in the parenthesis

you get -4[tex]y^{5}[/tex]  + 6y³  + 4y².   But where is the 8y² and -2y?

While Option B is equivalent, you can factor it out more and find the common factor of -2 to distribute among them as shown in option D

It is option D because distributing the -2y to each term solves to

-4[tex]y^{5}[/tex]  + 6y³   +  8y²  -2y.

Tai has 1/2 gallon of milk left in his
refrigerator. He pours the milk into
glasses that can each hold a 5/64 gallon.
How many glasses can Tai fill
completely with milk?

Answers

Answer:

He can completely fill six glasses, and there will be one glass 2/5 of the way full.

Step-by-step explanation:

-2×-7y=30
7×+4y=18
×=
y=​

Answers

Answer:

Answer is -7      Hope this helps :D

Step-by-step explanation:

The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 31 hours and the median is 27.2 hours. Twenty-four of the families in the sample turned on the television for 1616 hours or less for the week. The 7th percentile of the data is 16 hours. Based on the given information, determine if the following statement is true or false.

The 56th percentile is greater than or equal to 26 hours.

a. True
b. False

Answers

True I believe sorry if it is wrong but I think it is true.

Answer:

False

Step-by-step explanation:

A cosine function has a period of 5π6, an amplitude of 6, and a vertical translation 5 units down. The function is not reflected over the x-axis.


What is the equation for this cosine function?

Answers

Answer:

The equation is "[tex]y=6 \ Cos(\frac{12}{5}x)-5[/tex]". A further explanation is described below.

Step-by-step explanation:

The given values are:

Period,

B = [tex]\frac{5 \pi}{6}[/tex]

  = [tex]\frac{12}{5}[/tex]

Amplitude,

A = 6

Vertical translation down,

D = -5

As we know,

The equation of cosine function will be:

⇒  [tex]y=A \ Cos(Bx)+D[/tex]

On substituting the values in the above equation, we get

⇒  [tex]y=6 \ Cos(\frac{12}{5}x)+(-5)[/tex]

⇒  [tex]y=6 \ Cos(\frac{12}{5}x )-5[/tex]

Answer:

Step-by-step explanation:

Write the equation of this circle in standard form.

Answers

Answer:

x² + y² = 16

Step-by-step explanation:

(x-h)² + (y-k)² = r²   -- The standard form of equation of circle

(x-0)² + (y-0)² = 4²

I need help will mark you the brainliest

Answers

Answer:

i thinnk A

Step-by-step explanation:

what expressions are equivalent to 10 - 12​

Answers

Answer:

B

Step-by-step explanation:

(* ̄3 ̄)╭ When subtracting they both equal the same of -2

Answer:

B

Explanation:

When you multiply 2 and 5 (10) and 2 and -6 (-12), you get the same answer as 10 - 12.

the spinner above is used in a game. what is the theoretical probability of the given event with one spin? p(5)

a. 7/8
b. 1/8
c. 5/8
d. 0

Answers

B! 1/8 because it lands on one of the numbers each time and it’s numbered 1-8

The theoretical probability of the given event with one spin p(5) is,

⇒ p (5) = 1 / 8

What is mean by Probability?

The word probability refers to the likelihood of an event occurring. Probability means possibility. And,  It is branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to given that;

The spinner is used in a game.

Since, There are total 8 outcomes in spin.

Hence. The theoretical probability of the given event with one spin p(5) is,

⇒ p (5) = 1 / 8

Thus, The value of theoretical probability of the event with one spin p(5) is,

⇒ p (5) = 1 / 8

Learn more about the probability visit:

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PLEASE ANSWER ANY QUESTIONS ASAP THANK YOU SO MUCH

Answers

fw me on some points

SYSTEM OF EQUATIONS

The sum of three times Sophia's age and twice Nick's age is 73. Twice Sophia's age plus four times Nick's age is 86. How old is Sophia?

Answers

3s+2n=73
2s+4n=86


Multiply top equation by 2 and then subtract second equation

4s=60
Sophia is 15
Nick is 14

What is the area? Write your answer as a fraction or as a whole or mixed number.​

Answers

Answer:

81 or 20 1/4

Step-by-step explanation:

im not sure sorry

Answer:

[tex] \frac{1681}{4} [/tex]

or

[tex]105 \frac{1}{4} [/tex]

Step-by-step explanation:

[tex]10 \frac{ + 1}{ \times 4} [/tex]

10×4=40+1=41, that will be your numerator (number at the top of the fraction) and the denominator 4 will stay the same. (bottom number)

[tex] \frac{41}{4} [/tex]

the base and the height will remain the same.

Formula : base × height = Area

[tex] \frac{41}{4} \times \frac{41}{4} = \frac{1681}{16} [/tex]

16 goes into 1681 105 times remainder 1.

so as a mixed number it will be

[tex] 105 \frac{1}{4} [/tex]

Simplify: -6(x + 5) show work plz

Answers

Answer:

The answer is -6x - 30

Step-by-step explanation:

1) Expand by distributing terms.

[tex] - 6x - 6 \times 5[/tex]

2) Simplify 6 × 5 to 30.

[tex] - 6x - 30[/tex]

Thus, the answer is -6x - 30.

Answer:

-6x - 30

Step-by-step explanation:

Multiply using the distributive property.

-6x - 30

Hope this helps

Two angles are complementary. The measure of the first is (3x+14) and the measure of the second one is (5x-20). What are the measures of the two angles?

Answers

Answer:

x=17

Step-by-step explanation:Isolate the variable by dividing each side by factors that don't contain the variable. x=17. I hope this helps

Which is an equivalent expression for 6(2y+4)+5y?

please help

Answers

Answer:

17y+24

Step-by-step explanation:

simplify so the first step would be to multiply whats in the parentheses by the number outside in this case its 6 youd get:

12y+24+5y

then you simplify farther by adding like terms

17y+24

Which rectangle represents dilation by a scale factor of 2 from the rectangle's center?

Answers

Answer:

it’s D

Step-by-step explanation:

I took the test

Can someone help me with this problem number 4

Answers

Answer:

m = -11/7

Step-by-step explanation:

change equation into slope-intercept form:

7y = -11x + 2

y = -[tex]\frac{11}{7}[/tex]x + 2/7

slope is the coefficient of the 'x' term

Researchers conducted a study to determine whether the majority of community college students plan to vote in the next presidential election. They surveyed 650 randomly selected community college students and found that 55% of them plan to vote.

Which of the following are the appropriate null and alternative hypotheses for this research question?

A)
0: =0.50

: ≠0.50

B)

0: =0.50

: >0.50

C)

0: =0.55

: ≠0.55

D)

0: =0.55

: >0.55

Answer is:
B

Answers

Answer:

[tex]H_{0} = 0.5[/tex]

[tex]H_{a} > 0.5[/tex]

Option b

Step-by-step explanation:

Researchers conducted a study to determine whether the majority of community college students plan to vote in the next presidential election.

The null hypothesis is always an equalityu related to the expected, or tested value. In this question, the tested value is half of the students, a proportion of 0.5, that is: [tex]H_{0} = 0.5[/tex]

The alternate hypothesis is related to the test we are taking. In this question, we are testing if the majority of the students plan to vote, that is, if the proportion of the students that plan to vote is higher than 0.5. So [tex]H_{a} > 0.5[/tex]

So the correct answer is given by option B.

. Robbie decides to make 12 batches of chicken noodle soup. How much ground black pepper should he use? ( THERE ARE 1/8 TEASPOON OF GROUNDPM PEPPER IN ONE BATCH) pls put in fraction form​

Answers

the answer for your question is 1 1/2

How many solutions does x2 - 2x + 9 = 0 have and what type are they? Do NOT find the
actual solutions.

Answers

Answer:

3

Step-by-step explanation:


What is the measure of angle R?

Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.

mZR
=

Answers

Answer:

m<R = 22.62°

Step-by-step explanation:

Reference angle = R

Opposite = 5 cm

Hypotenuse = 13 cm

Apply the trigonometric function SOH:

Sin R = Opp/Hyp

[tex] Sin (R) = \frac{5}{13} [/tex]

[tex] R = sin^{-1}(\frac{5}{13}) [/tex]

R = 22.6198649°

m<R = 22.62° (nearest hundredth)

Consider the expression

Answers

PHOTOMATHH !!!!!! Take a screenshot of it it’s quick

Raul borrows $600 at an interest rate of 8% per year for 4 years. How much simple interest will he have to pay?

Answers

__________________________________

A = P × i × n = $600 × 8% × 4 Years= $192= $600 + $192= $2,619Raul Will Have To Pay $2,619

__________________________________

3t−18=4(−3−
4
3

t)

Answers

Answer: 0.034

Step-by-step explanation:3t-18=4(-3-43t)

3t-18=-12-172t

3t+172t=-12+18

175t/175=6/175

t=0.034

What is the median of this set of data?

362, 187, 211, 298, 331, 250, 347, 199

Answers

Answer:

274

Step-by-step explanation:

Hey There!

So if you didnt know the median is the middle number ( in value) of the set

So first we would like to arrange the numbers in order from least to greatest

187 , 199 , 211 , 250 , 298 , 331 , 347 , 362

Then we take the middle number(s)

if there is just one then that is the answer but if there is two than we add them together and divide that by 2

In this case there are two which would be 250 and 298

So we add them together

250+298=548

Then we just divide that by 2

[tex]\frac{548}{2} =274[/tex]

Therefore the median is 274

hope this helps :)

Step-by-step explanation:

l hope this answer is helpful to you

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