For each problem clearly describe the conditional distribution of each coordinate given the others. Then describe the procedure for running Gibbs sampling to sample from the joint distribution. Assume that Gibbs sampling works for continuous densities as well as discrete distributions. Guess the conditional from the structure of the joint distribution. Avoid doing integration as much as possible. Use your knowledge of the all the named one dimensional distributions/ densities.

a. Sample from the mixed joint pmf/pdf:

f(p, n) = p(1 - p)^-1, 0

You will need one integration to describe the density of p given N = n.

b. Sample from the joint density: f(p, q, r) =1/ Żpar, 0 < P, q ,r <1.

You will need one easy integration. What is special about this joint density?

Answer:

Step-by-step explanation:i really am lost,

The work rate for the associate is 5.3 hours.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given; Jane can paint the office by herself in 7 hours.

with an associate, she can paint the office in 3 hours.

The combined work rate is 3 hours per office.

WE need to find the work rate for the associate

Let the expression for the work rate be;

1/A+1/B= 1/T

1/7+1/B=1/3

1/B=1/3-1/7

1/B= 8-4/21

1/B= 4/21

B= 21/4

B=5.3 hours

Therefore, the work rate for the associate is 5.3 hours.

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Answer:

The probability that a defective ball bearing was manufactured on a Friday = 0.375

Step-by-step explanation:

Let the event of making a mistake = M

The event of making a precision ball bearing production on Monday = Mo

The event of making a precision ball bearing production on Tuesday = T

The event of making a precision ball bearing production on Wednesday = W

The event of making a precision ball bearing production on Thursday = Th

The event of making a precision ball bearing production on Friday = F

the conditional probability of making a manufacturing mistake in its precision ball bearing production is 4% on Tuesday, P(M|T) = 4% = 0.04

4% on Wednesday, P(M|W) = 0.04

4% on Thursday, P(M|Th) = 0.04

8% on Monday, P(M|Mo) = 0.08

and 12% on Friday = P(M|F) = 0.12

The Company manufactures an equal amount of ball bearings (20 %) on each weekday, Hence, the probability that a random precision ball bearing was made on a particular day of the week, is mostly the same for all the five working days.

P(Mo) = 0.20

P(T) = 0.20

P(W) = 0.20

P(Th) = 0.20

P(F) 0.20

The probability that a defective ball bearing was manufactured on a Friday = P(F|M)

P(F|M) = P(F n M) ÷ P(M)

P(F n M) = P(M n F)

P(M) = P(Mo n M) + P(T n M) + P(W n M) + P(Th n M) + P(F n M)

We can obtain each of these probabilities by using the expression for conditional probability.

P(Mo n M) = P(M|Mo) × P(Mo) = 0.08 × 0.20 = 0.016

P(T n M) = P(M|T) × P(T) = 0.04 × 0.20 = 0.008

P(W n M) = P(M|W) × P(W) = 0.04 × 0.20 = 0.008

P(Th n M) = P(M|Th) × P(Th) = 0.04 × 0.20 = 0.008

P(F n M) = P(M|F) × P(F) = 0.12 × 0.20 = 0.024

P(M) = P(Mo n M) + P(T n M) + P(W n M) + P(Th n M) + P(F n M)

P(M) = 0.016 + 0.008 + 0.008 + 0 008 + 0.024 = 0.064

P(F|M) = P(F n M) ÷ P(M)

P(F n M) = P(M n F) = 0.024

P(M) = 0.064

P(F|M) = P(F n M) ÷ P(M) = (0.024/0.064) = 0.375

Hope this Helps!

Answer:

ED = 8

Step-by-step explanation:

AC = 21 which means AE is 1/3 of the length of AC.

So, ED must also be 1/3 of the length of BC.

1/3 x 24 = 8

Answer:

24

Step-by-step explanation:

Y is 60% of 40

Equation: Y = P% * X

Solving our equation for Y

Y = P% * X

Y = 60% * 40

Converting percent to decimal:

p = 60%/100 = 0.6

Y = 0.6 * 40

Y = 24

Answer:

V=16x^5+8x^4+56x^3.

Step-by-step explanation:

The volume of the rectangular prism is V=16x^5+8x^4+56x^3.

Formula for rectangle prism: V=whl

Formula: L*W*H

Answer: V=16x^5+8x^4+56x^3

Hope this helps.

Answer:

45

please see the attached picture for full solution

hope it helps

Good luck on your assignment

Answer:

Step-by-step explanation:

Since; the density function diagrams were not included in the question; we will be unable to determine the  best which depicts this problem.

However;

Let use X to represent the time required for the delivery.

Then X~N(3.8 ,0.8)

i.e

E(x) = 3.8

s.d(x) = 0.8

NOW; P(x>4) = P(X-3.8/0.8 > 4-3.8/0.8)

= P(Z > 0.25)

= 1-P(Z < 0.25)

=1 - Φ (0.25)

= 1 - 0.5987  ( from Normal table  Φ (0.25) = 0.5987 )

= 0.4013

Thus;  the probability a single delivery would take more than 4 hours is 0.4013

What is the z value corresponding to the interval boundary?

The z value is calculated as:

[tex]z = \dfrac{X- \mu}{\sigma}[/tex]

[tex]z = \dfrac{4- 3.8}{0.8}[/tex]

z = 0.25

Answer:

x=4

Step-by-step explanation:

think of the equation like this: you have to do the inverse(opposite) operations so for adding you would subtract it. So for the adding 3 you would subtract it from both sides of the equation and get X=4

Answer:

4x²

Step-by-step explanation:

Your equation is 4x² - 6x² + 7x² - 20x² + 19x².

Since they all have the same variable, simply combine them all to find your answer.

4x² - 6x² + 7x² - 20x² + 19x²

-2x² + 7x² - 20x² + 19x²

5x² - 20x² + 19x²

-15x² + 19x²

4x²

Answer:

2.54 miles/hr

2.04 miles/hr

Step-by-step explanation:

Given: Distance between the two towns = 1100 miles

Difference between speeds = [tex]\frac{1}{2}[/tex] miles/hr

Total time when they meet = 240 hours

To find:

Let distance traveled by first group = [tex]x[/tex] miles.

Now, the distance traveled by second group = (1100-[tex]x[/tex]) miles/hr

The relation between Speed, Time and Distance is given as:

[tex]\text{Speed =} \dfrac{\text{Distance}}{\text{Time}}[/tex]

Let speed of first group = [tex]S_1[/tex]

[tex]S_1 = \dfrac{x}{240}[/tex]

Let speed of second group = [tex]S_2[/tex]

[tex]S_2 = \dfrac{1100-x}{240}[/tex]

As per question, [tex]S_1[/tex] = [tex]S_2[/tex] + [tex]\frac{1}{2}[/tex]

[tex]\dfrac{x}{240} = \dfrac{1100-x}{240} + \dfrac{1}{2}\\\Rightarrow \dfrac{x}{240} - \dfrac{1100-x}{240} = \dfrac{1}{2}\\\Rightarrow \dfrac{x-1100+x}{240} = \dfrac{1}{2}\\\Rightarrow 2x - 1100 = 120\\\Rightarrow 2x = 1220\\\Rightarrow x = 610 ft[/tex]

Now,

[tex]S_1 = \dfrac{x}{240}[/tex]

Putting value of [tex]x[/tex]:

[tex]S_1 = \dfrac{610}{240}\\\Rightarrow S_1 = 2.54\ miles/hr[/tex]

Similarly, putting value of [tex]x[/tex] in [tex]S_2[/tex]:

[tex]S_2 = \dfrac{1100-610}{240}\\\Rightarrow S_2=\dfrac{490}{240}\\\Rightarrow S_2 = 2.04\ miles/hr[/tex]

The scale for the second values is 56/8 = 7

C = 3 x 7 = 21

C= 21

Answer:

76 % of babies will be born out of​ wedlock in the [tex]81^{st}[/tex] year

Step-by-step explanation:

Given:  In​ 1990, 28 % of babies in the United States were born to parents who were not married. This increased by approximately 0.6 % per year.

To find: year when 76 % of babies born out of​ wedlock

Solution:

A sequence is said to be in arithmetic progression if the difference between the terms is same.

For a sequence with first term as 'a' and common difference as 'd', the nth term is given by [tex]a_n=a+(n-1)d[/tex]

The given situation also forms an arithmetic progression with  [tex]a=28\,,\,d=0.6[/tex]

Also, put [tex]a_n=76[/tex]

So,

[tex]a_n=a+(n-1)d\\76=28+(n-1)(0.6)\\76-28=0.6(n-1)\\48=0.6(n-1)\\\frac{48}{0.6}=n-1\\\\80=n-1\\n=80+1\\n=81[/tex]

So, 76 % of babies will be born out of​ wedlock in the [tex]81^{st}[/tex] year

Answer:

Option (A)

Step-by-step explanation:

Two inequalities have been given as,

y > 3x + 6 --------(1)

y < 3x - 7 ------(2)

Inequality (1) shows the solution area shaded in blue, means all the solutions for the inequality will lie in the blue area.

Similarly, solutions of inequality (2) will lie in red area.

No common area for the inequalities.

Therefore, system of inequalities will have no solution.

Option (A) will be the answer.

Answer: angle A = 72 and angle C = 72

Step-by-step explanation:

Angle A and C are opposites so they have to equal each other so do the equation 3y+27=5y-3. y would come out to be 15 and so to find the angles you would replace y with 15.

Answer:

10

Step-by-step explanation:

[tex] \frac{ \sqrt{75a} + \sqrt{12a} + \sqrt{27a} }{ \sqrt{3a} } \\ \frac{ \sqrt{(25 \times 3)a} + \sqrt{(4 \times 3)a} + \sqrt{(9 \times 3)a} }{ \sqrt{3a} } \\ \frac{ 5\sqrt{3a} + 2 \sqrt{3a} + 3\sqrt{3a} }{ \sqrt{3a} } \\ \frac{(5 + 2 + 3) \sqrt{3a} }{ \sqrt{3a} } = 10[/tex]

Answer: See below

Step-by-step explanation:

My old math notebook had simillar question,hope that help

√75a+√12a-√27a/√3a

=√a(3*25)+√a(3*4)+√a(3*9)/√3a

=√25*√3a+√4*√3a+√9*√3a/√3a

=(5+2+3)√3a/√3a

=5+2+3=10

Answer:

The expression created is: [tex]3x^2+3x+8x-7[/tex]

Simplified, we obtain : [tex]3x^2+11x-7[/tex]

Step-by-step explanation:

We are to create an expression that satisfies the following conditions

Let the two like terms be 3x and 8x

Let the integer term = -7

Let the other term [tex]=3x^2[/tex]

Our written expression is therefore:

[tex]3x^2+3x+8x-7[/tex]

We simplify the expression by solving the like terms for a single term

[tex]3x+8x=11x\\$Therefore\\3x^2+3x+8x-7=3x^2+11x-7[/tex]

Answer:

  [tex]d=\sqrt{r_1^2+r_2^2-2r_1r_2\cos(u_2-u_1)}[/tex]

Step-by-step explanation:

The Law of Cosines gives an immediate result. No translation to Cartesian coordinates is necessary. That law makes use of the angle between the vectors, u2-u1

  [tex]d^2=r_1^2+r_2^2-2r_1r_2\cos(u_2-u_1)\\\\\boxed{d=\sqrt{r_1^2+r_2^2-2r_1r_2\cos(u_2-u_1)}}[/tex]

Answer:

X=0 and Y= 4(2i-1)/5

Step-by-step explanation:

Here is my solution, assuming that the equation equals 0. For y, just remember the definition of complex numbers and multiply by its conjugate.

The value of x and y are -8/7 and -4 respectively if (x + yi) + 2(3x - y) + 4i = 0.

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number:

(x + yi) + 2(3x - y) + 4i = 0

After arranging:

x + yi + 6x - 2y + 4i = 0

7x - 2y + yi + 4i = 0

7x - 2y + (y + 4)i = 0

7x - 2y = 0

y + 4 = 0

This is the linear equation in two variables:

Plug y = -4 in the other equation:

7x - 2(-4) = 0

7x = -8

x = -8/7

y = -4

Thus, the value of x and y are -8/7 and -4 respectively if (x + yi) + 2(3x - y) + 4i = 0.

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Answer: 7,864,320

Step-by-step explanation:

Because the doubling time is 20 minutes, the bacteria would have gone through binary fission(cell division in bacteria) 18 times after 6hours(6*60/20)

Nt=N0 * 2^n

N0=starting population

n=number of times bacteria divide

So

30*2^18=7,864,320

Answer:

Step-by-step explanation:

The probability that the forester does not get the seedlings is 1/2 if the mean density of seedlings is 5 per square metre.

Density means the area within which a substance is collected or taken.

We have been given the mean density =5 square metre.

And we  have to calculate the probability that the forester will not get any seedlings.

So the probability that he will get the seedlings will be=5/10

which is 1/2

So the probability that he will not get the seedlings will be 1-1/2

that is 1/2.

Hence the probability that he will not get seedlings will be 1/2.

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Answer:

2.96 seconds

Step-by-step explanation:

Let H(x) = zero and solve for "x".

43 - 4.9x² = 0

4.9x²=43

x²=8.77

x=2.96

therefore, approximately when x=2.96seconds, the rock strike the ground.

Answer:

Since Interquartile Range consider the middle values in the data set, i.e. 50%, it is not affected by outliers or extreme values. While other statistics mean, standard deviation and range are all affected by outliers or extreme values.

Step-by-step explanation:

hope this helps you :) can you help me please northc04 :(

Answer:

The answer is Interquartile Range. I know this is the right answer is because I got it right on a quiz.

Answer:

(a)(B)Yes. This is a legitimate finite probability model because each probability is between 0 and 1 , and all sum to 1 .

(b)P(20‑ to 24‑year‑old who is married)=0.027

(c)P(20–24 year old)=0.26

(d)P(married)=0.398

Step-by-step explanation:

Given the probability model below:

[tex]\left\begin{array}{|c|c|c|c|c|}$Age in years& 20 - 24& 25 - 29& 30 - 34& 35 - 39\\$Never married& 0.227& 0.156& 0.089& 0.054\\ $Married &0.027& 0.086& 0.137& 0.148\\$Widowed/divorced/separated &0.006 &0.015& 0.022& 0.033\end{array}\right\\[/tex]

(a)

0.526+0.398+0.076=1

Therefore this is a legitimate finite probability model because each probability is between 0 and 1 , and all sum to 1 .

(b) The probability that the person chosen is a 20‑24-year‑old who is married

P(20‑ to 24‑year‑old who is married)=0.027

(c)Probability that the person chosen is 20 – 24 years old

P(20–24 year old)=0.227+0.027+0.006=0.26

(d)Probability that the person chosen is married

Answer:

8.62% probability that all have the same color

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the marbles are selected is not important. So we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

What is the probability that all have the same color?

Desired outcomes:

Either all red(from a set of 9), all white(from a set of 9) or all blue(from a set of 8). So

[tex]D = C_{9,3} + C_{9,3} + C_{8,3} = \frac{9!}{3!6!} + \frac{9!}{3!6!} + \frac{8!}{3!5!} = 224[/tex]

Total outcomes:

3 marbles, from a set of 9 + 9 + 8 = 26. So

[tex]T = C_{26,3} = \frac{26!}{3!23!} = 2600[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{224}{2600} = 0.0862[/tex]

8.62% probability that all have the same color

Answer:

As there are six seats in a row and the first person in the row is a woman and the people alternate woman, men, the possibility is

W

M

W

M

W

M

in that order.

Now as we four women, three seats for women can be filled in

X

4

P

3

=

24

ways

and similarly as we four men, three seats for men can be filled in

X

4

P

3

=

24

ways

Hence, total

24

×

24

=

576

permutations.

Step-by-step explanation:

Answer:

Greater x =+ 7

Lesser x = -7

Step-by-step explanation:

G(x) = -10x2+ 490

Let the left side = 0

So we have

0= -10x2+ 490

Solving the above now by allowing the variable with the coefficient of x cross the equal sign.

10x²= 490

Dividing by 10

X²= 490/10

X² = 49

Taking the root of both sides

X= √49

X = + 7or -7

Bigger x =+ 7

Smaller x = -7