Astronomers treat the number of stars X in a given volume of space as Poisson random variable. The density of stars in the Milky Way Galaxy in the vicinity of our solar system is one star per 16 cubic light-years, on average. NOTE: Light-years is a distance measure. 7. What is the probability of exactly two stars in 16 cubic light-years? 8. What is the probability of three or more stars in 16 cubic light-years? 9. How many stars would be expected in 4 cubic light years? 10. How many stars would be expected in t cubic light years? 11. How many cubic light-years of space must be studied so that the probability of one or more stars exceeds 0.95? HINT: let `t' represent the unknown region of space, then nd the `t' that gives you the relevant probability.

Answers

Answer 1

Answer:

Explained below.

Step-by-step explanation:

The random variable X is defined as the number of stars in a given volume of space.

[tex]X\sim \text{Poisson}\ (\lambda=1)[/tex]

The probability mass function of X is:

[tex]p_{X}(x)=\frac{e^{-\lambda}\lambda^{x}}{x!}[/tex]

(7)

Compute the probability of exactly two stars in 16 cubic light-years as follows:

[tex]P(X=2)=\frac{e^{-1}\times 1^{2}}{2!}=\frac{e^{-1}}{2}=\frac{0.36788}{2}=0.18394\approx 0.184[/tex]

(8)

Compute the probability of three or more stars in 16 cubic light-years as follows:

[tex]P(X\geq 3)=1-P(X<3)\\\\=1-P(X=0)-P(X=1)-P(X=2)\\\\=1-\sum\limits^{2}_{x=0}[\frac{e^{-1}\times 1^{x}}{x!}]\\\\=1-0.36788-0.36788-0.18394\\\\=0.0803[/tex]

(9)

In 16 cubic light years there is only 1 star.

Then in 1 cubic light years there will be, (1/16) stars.

Then in 4 cubic light years there will be, 4 × (1/16) = (1/4) stars.

(10)

In 16 cubic light years there is only 1 star.

Then in 1 cubic light years there will be, (1/16) stars.

Then in t cubic light years there will be, [t × (1/16)] stars.


Related Questions

A pet store has cats. Here are their weights (in pounds).
8, 5, 14, 12, 7
Find the mean weight of these cats.
If necessary, round your answer to the nearest tenth.

Answers

9.2. Because you add up all of the numbers then divide by how many numbers you have. 8+5+14+12+7= 46 then divide by 5.

Answer: 9.2

Step-by-step explanation: 8+5+14+12+7. = 46

46÷5= 9.2

Graph (f(x)+-2((x+3)(x-1). Label the x intercepts, vertex and axxis of symmetry

Answers

Answer: x-intercepts: (-3,0), (1,0)

              vertex: (-1,8)

              axis of symmetry: x = -1

Step-by-step explanation:

PLEASE, I NEED HELP!!!!
MATHS!!!

Answers

Answer:

a

Step-by-step explanation:

can you guys help me pls what is [34 + (9×2)]÷2= what is it pls help​

Answers

Answer:

306

Step-by-step explanation:

What is the value of 5 Z when Z is equal to 2

Answers

Answer:

10?

Step-by-step explanation:

5 times Z= 5x 2= 10

can someone please help me :)

Answers

Answer:

C

Step-by-step explanation:

These pairs are both interior angles and are consecutive because they are divided by a transversal.

the answer is c! i hope this helps!!

A______ is a value, usually in the form of a letter or symbol, that can change or that represents an unknown quantity.

Answers

Answer:

Variable

Step-by-step explanation:

The range of the following relation R(3,-2), (1, 2), (-1, -4),(-1, 2)} is {-1, 1, 3) {-1, -1, 1.3} (-4, -2, 2. 2) (-4, -2.2 without it saying brainly plus​

Answers

Answer:

{-4, -2, 2}

Step-by-step explanation:

Given relation

R {(3,-2), (1, 2), (-1, -4),(-1, 2)}

Its range is the set of second values in the pairs

{-2, 2, -4}

In the ascending order

{-4, -2, 2}

Answer:

{-4, -2, 2}

Step-by-step explanation:

The relation is {(3, -2), (1, 2), (-1, -4),(-1, 2)}

The range is all possible y values apart from any duplicates.

y = -2, 2, -4, 2

Removing all duplicates we get.

y = -2, 2, -4

Put them in order.

y = -4, -2, 2

Best of Luck!

The sales tax on a used car is​ $102​, and the sales tax rate is ​%5. Find the purchase price ​(the price before taxes are​ added).

Answers

Answer:

.04p = 102

p = 2550

The original price is $2550.

which is greater 1/8 or 3/20

Answers

Answer:

1/8

Step-by-step explanation:

Given the parallel lines and transversal determine the value of x. Plz help due in an hour

Answers

We know that 2x + 10 is equal to 86 + x because of vertically opposite angles and from this we can form an equation: 2x + 10 = x + 86
Firstly, take away x from both sides to get x + 10 = 86
Now take away 10 from both sides and we get x = 76
Hope this helps and a Brainliest would be very appreciated

A water tower holds 26400 gallons of water. The water company can fill the tower at a rate of 20 gallons per minute,
How many hours would it take the water company to all the tower if it is completely empty?
o 22 hours
24 hours
220 hours
0 440 hours

Answers

Answer: 22 hours

Step-by-step explanation: 26400/20 is 1320 and 1320/60 is 22

A study was conducted on the effects of divorce. Researchers gathered data from a random sample of 5,125 adults and measured quite a few variables, in addition to the explanatory variable of divorce and the response variable of shorter life span. According to a newspaper article summarizing the study, those who divorced were more likely to be less physically active, at an unhealthy weight, and smokers. Those who were married were about 15% more likely to be deceased. What conclusion can we draw from this study? Explain. (5 points) We can infer a cause-and-effect relationship because the sample was selected randomly. We cannot infer a cause-and-effect relationship because we do not have a control group. We can infer a cause-and-effect relationship because multiple variables were included. We cannot infer a cause-and-effect relationship because the treatments imposed were not blocked correctly. We cannot infer a cause-and-effect relationship because treatments were not assigned randomly.

Answers

Answer:

We can infer a cause-and-effect relationship because multiple variables were included.

Step-by-step explanation:

The multiple attributes for the divorced ones are

1) less physically active

2) an unhealthy weight,

3) smokers.

The attribute showing the % of the married is

1) death

So when we compare the two groups married and divorced we see different variables are involved in evaluating the percentage.

This shows a cause and effect involving multiple variables.

In cause and effect one variable is dependent and the other is independent.

The cause is the independent variable and effect is the dependent variable.

CAUSE                          EFFECT

Married                         Death

Divorced                     1) less physically active

                                  2) an unhealthy weight,

                                     3) smokers.

Answer:

We cannot infer a cause-and-effect relationship because treatments were not assigned randomly.

Glimepiride 2mg OD is ordered in a prescription, your pharmacy has 4mg stocks on hand. How much tablet will you give? 2mg​

Answers

At first, 1 to 2 milligrams (mg) once a day. Your doctor may adjust your dose until your blood sugar is controlled. However, the dose is usually not more than 8 mg per day.

The total amount of money that he had deposited into his account at the end of March is what

Answers

Answer: 1,200.65+ 985.43+ 1,200.23= 3,386.31

Step-by-step explanation:

Multiply.
(2x + 4)(x - 4)

Answers

Answer:

-2x-16

Step-by-step explanation:

so what you are going to do for this is use the distributive property. 2x will be multiplied by x and -4. then you will take 4 and multiply x and -4. then you combine your alike terms. 2x-8x+4x-16 you should get -2x-16

The equivalent expression after multiplying is 2(x² - 2x - 8).

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(2x + 4) (x - 4)

Remove the parenthesis.

2x² - 8x + 4x - 16

Add like terms.

2x² - 4x - 16

Taking out the common factor.

2 (x² - 2x - 8)

Thus,

The final expression is 2(x² - 2x - 8).

Learn more about expressions here:

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Find the solution of the system of equations

4x-8y=44
2x+4y=-6

Answers

It is easiest to solve this system by elimination.

4x-8y=44

(2x+4y=-6) -2    ----> multiply the second equation by -2 to create equations where the x coefficients are opposites

     4x-8y=44

(+) -4x-8y=12

-16y=56

y = -7/2

now substitute the value of y into one of the above equations and solve for x

4x – 8(-7/2) = 44

4x + 28 = 44

4x = 16

X = 4

So, the solution is (4, -7/2)

The solution of the  system of equations 4x-8y=44 and 2x+4y=-6is (4, -3.5).

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

The given system of equation is 4x-8y=44 ...(1)

and 2x+4y=-6...(2)

To eliminate y term we have to multiply equation 2 with 2.

4x+8y=-12..(3)

Now add equation 1 and 3.

4x-8y+4x+8y=44-12

8x=32

Divide both sides by 8

x=4

Now plug in x value in equation 1

4(4)-8y=44

16-8y=44

Subtract 16 from both sides

-8y=44-16

-8y=28

Divide both sides by 8

y=-28/8

y=-7/2

=-3.5

Hence, the solution of the  system of equations is (4, -3.5).

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How do I solve -0.4r=16?

Answers

Answer:

r = -40

Step-by-step explanation:

1. Move constants to the other side of the equation

r = 16/-.04

2. Simplify (by calculator)

You can use a calculator and plug in 16/-.04

r = -40

2. Simplify (by fraction)

You can turn -.4 into a fraction.

-.04 = - 4/10

r = 16/-(4/10)

r = 16*10/-4

r = -40

An elevator steadily descends 500 feet in 20 seconds. How would you express the change in the​ elevator's height per​ second?

Answers

Answer:

The elevator goes 25 feet per second.

Step-by-step explanation:

The elevator goes 500 feet every 20 seconds so to find how hogh it gets to in 1 second, you have to use the equation 500 divided by 20 to get 25.

Hope this helps idk if it will tho.

Given m||n, find the value of x.
t
>m
(7x-1)
(9x+5)

Answers

Answer:

Step-by-step explanation:

-13m-or+t m(484m+63t)/63m

which 1 is the answer

Answers

Answer:

The second one

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

B is the answer have a great day

3 (-2x + 1)
What does this equal

Answers

Answer:

-6x+3

Step-by-step explanation:

When you solve this you have to use the distributive property. Your answer would be -6x + 3

2. Given 3,989, 825;
round to the nearest
ten thousand, hundreds, and thousands

Answers

Answer:

then thousand -3,990,000

hundred -3,989,800

thousands-3,990,000

hope this helped :)

plese help im in 2nd grade and this is really hard all the kids in my class know it but me​

Answers

Answer:

This isn't in second gradee- x-x

Step-by-step explanation:

Answer: For x such that 0<x<(pie/2), the expression:

[square-root(1-cos^2(x)]/sinx + [square-root(1-sin^2(x)]/cos(x)

is equivalent to,

F. 0

G. 1

H. 2

J. -tan(x)

K. sin2x

The answer is H.

Step-by-step explanation:

When Michael Jordan retired from basketball he had the third highest scoring total in NBA history at 32,292 points an average 30 points per game for his whole career. However, Kobe Bryant passed Jordan on the list for third place with 33,643 points before COBE retired. If Michael Jordan started playing again, how many games would he have to play to catch cobia for third place? (You must write an equation and show you were to support your answer)

Answers

9514 1404 393

Answer:

  46 games

Step-by-step explanation:

Let g represent the number of games played at 30 points per game. Then Jordan's total score would be

  32292 +30g

We want to find the value of g that makes this total 33,643:

  32292 +30g = 33643

  30g = 1351

  g ≈ 45.03

Jordan would have to  play 46 games to regain 3rd place.

_____

After 45 games, Jordan's point total would be 33,642, which is 1 point short of Bryant's record.

PLEASE HELP!!! ILL GIVE BRANLIEST *EXTRA POINTS* dont skip :((

Answers

Answer:

A

Step-by-step explanation:

it just is.

Answer:

a sq rt 38

Step-by-step explanation:

a=6.1

b=5.9

c=6.7

d=6.9

a is closet to dot between 6 and 7

What number when divided by 10 to the second power yields a quotient of 0.1?

Answers

Answer:

1

Step-by-step explanation:

1 ÷ 10 = 0.1

hope this helped

俄國採購總共工作有關廣告㷣菇菇過各式各樣奴

In a casino in Blackpool there are two slot machines (machine 1 and machine 2): one that pays out 10 % of the time, and one that pays out 20 % of the time. Obviously, you would like to play on the machine that pays out 20% of the time but you do not know which of the two machines is the more generous. You thus adopt the following strategy: you assume initially that the two machines are equally likely to be the generous machine. You then select one of the two machines at random (this turns out to be machine 1) and put a coin into it. Given that you loose that first bet estimate the probability that machine 1 is the more generous of the two machines
What do I know?
What do I want to find out?
What do I expect the answer to be?
How do I go from what I know to what I want to find?
Is the answer consistent with what I expected?

Answers

Answer:

Given that;

a)

2 machines, 1 and 2

Machine 1

pays 10% of times when the machine is generous

So the probability that the machine 1 pays given that its generous is

P (Pays/machine 1 is generous) = 10% = 0.10

Machine 2  

pays 20% of times when its generous

i.e the probability that the machine pays given that its generous is;

P (Pays / machine 2 is generous) = 20% = 0.20

Also we assume there is equal chance of being generous

i.e

P(machine 1 is generous) = P(machine 2 is generous ) = 0.5  

b)

this is to help obtain the probability that machine 1 is generous given that the player loose in the first bet,

i.e P(machine 1 is generous / lost)  

c)

Since, the probability that the machine is generous is 0.5,

it can be said that there is 50% chance that machine 1 is generous when the player loses the first bet

d)

therefore The required probability is calculated as;

P(machine 1 is generous/lost) = p(machine 1 is generous ∩ lost) / p (lost)

= [p(lost/machine 1 is generous) × p(machine 1 is generous)] / [{(1-p(pays/machine 1 is generous)) × p(machine 1 is generous)} + {((1-p(pays/machine 2 is generous)) × p(machine 2 is generous)}]

= [(1 - p(pays/machine 1 is hereous)) × p(machine 1 is generous)] × [(( 1- 0.10) × 0.5) + ((1 - 0.20) × 0.5)]

= ( 1- 0.10) × 0.5) / 0.85

= 0.5294

so  the probability that the player loses the first bet given that the machine is generous is 0.5294

e)

Since the gotten probability that the player loses the first bet given that machine 1 is generous is close to 0.50 then it can be said that the probability is consistent with the expectations.

Problem
What is the slope of the line that contains these points?
***********
slope:

Answers

Answer: -8

Explanation: the formula to find slope is

y1 - y2/x1 - x2

When you substitute the values in this formula, you get

= 36 - 12/8 - 11
= 24/-3
= -8

Therefore, the slope is -8

explain why a student who runs 3/4 mile in 6 minutes is faster than a student who runs 1/2 mile in 5 minutes.​

Answers

Answer:

A student who runs 3/4 mile in 6 minutes is faster than a student who runs 1/2 mile in 5 minutes because when you simplify both fractions to per minute, the student who ran 3/4 mile in 6 minutes (1/8 mile per min) ran faster than the student who ran 1/2 mile in 5 minutes (1/10mile in 1 min).

Step-by-step explanation:

[tex]\frac{3/4mile}{6min}[/tex] divided by 6 to get per min =

1/8 mile per min

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