MATHEMATICS COLLEGE

consider a sequence of independent tosses of a biased coin at times k=0,1,2,…,n. On each toss, the probability of Heads is p, and the probability of Tails is 1−p.A reward of one unit is given at time k, for k∈{1,2,…,n}, if the toss at time k resulted in Tails and the toss at time k−1 resulted in Heads. Otherwise, no reward is given at time k.Let R be the sum of the rewards collected at times 1,2,…,n.We will find E[R] and var(R) by carrying out a sequence of steps. Express your answers below in terms of p and/or n using standard notation. Remember to write '*' for all multiplications and to include parentheses where necessary.We first work towards finding E[R].1. Let Ik denote the reward (possibly 0) given at time k, for k∈{1,2,…,n}. Find E[Ik].E[Ik]=2. Using the answer to part 1, find E[R].E[R]=The variance calculation is more involved because the random variables I1,I2,…,In are not independent. We begin by computing the following values.3. If k∈{1,2,…,n}, thenE[I2k]=4. If k∈{1,2,…,n−1}, thenE[IkIk+1]=5. If k≥1, ℓ≥2, and k+ℓ≤n, thenE[IkIk+ℓ]=6. Using the results above, calculate the numerical value of var(R) assuming that p=3/4, n=10.var(R)=

Answers

Answer 1

Answer:

Answer:

1. p*(1-p)

2. n*p*(1-p)

3. p*(1-p)

4. 0

5. p^2*(1-p)^2

6. 57/64

Step-by-step explanation:

1. Let Ik denote the reward (possibly 0) given at time k, for k∈{1,2,…,n}. Find E[Ik].

E[Ik]= p*(1-p)

2. Using the answer to part 1, find E[R].

E[R]= n*p*(1-p)

The variance calculation is more involved because the random variables I1,I2,…,In are not independent. We begin by computing the following values.

3. If k∈{1,2,…,n}, then

E[I2k]= p*(1-p)

4. If k∈{1,2,…,n−1}, then

E[IkIk+1]= 0

5. If k≥1, ℓ≥2, and k+ℓ≤n, then

E[IkIk+ℓ]= p^2*(1-p)^2

6. Using the results above, calculate the numerical value of var(R) assuming that p=3/4, n=10.

var(R)= 57/64

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A computer manufacturer built a new facility for assembling computers. There were construction and new equipment costs. The company paid for these costs and made combined profits of $40 million after 4 years, while profits increased $30 million per year. Select the correct graph of this function. (2 points)A)There is a graph of a line that has a y intercept that is approximately $80 million and passes through the point of approximately x equals 2 years and y equals $140 million.B)There is a graph of a line that has a y intercept that is approximately negative $80 million and an x intercept that is approximately 2.7 years.C)There is a graph of a line that has a y intercept that is approximately negative $45 million and an x intercept that is approximately 2 years.D)There is a graph of a line that has a y intercept that is approximately negative $45 million and an x intercept that is approximately 0.6 years.

Are they equal or diffrent angles

Answers

equal because the parallel lines :)

For his long distance phone service, Bill pays a $3 monthly fee plus 11 cents per minute. Last month, Bill's long distance bill was $16.09. For how many minutes was Bill billed?

Answers

Answer:

1.19 minutes

Step-by-step explanation:

First, subtract the $3 monthly fee:

16.09 - 3

= 13.09

Then, divide this by 11:

13.09/11

= 1.19

So, he was billed for 1.19 minutes

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y 2 ( y 2 − 4 ) = x 2 ( x 2 − 5 ) , ( 0 , − 2 ) (devil's curve) y2(y2-4)=x2(x2-5), (0,-2) (devil's curve)

Answers

Answer:

y = -2

Step-by-step explanation:

To find the equation of the tangent we apply implicit differentiation, and then we take apart dy/dx

The equation is

$y^2(y^2-4)=x^2(x^2-5)$

implicit differentiation give us

$(d)/(dx)[y^2(y^2-4)=x^2(x^2-5)]\n\n2y(dy)/(dx)(y^2-4)+y^2(2y(dy)/(dx))=2x(x^2-5)+x^2(2x)\n\n4y^3(dy)/(dx)-8y(dy)/(dx)=2x^3-10x+2x^3\n\n(dy)/(dx)=(4x^3-10x)/(4y^3-8y)$

But we know that

$m=(dy)/(dx)\ny=mx+b$

Hence, for the point (0,-2) and by replacing for dy/dx

$m=(dy)/(dx)_((0,-2))=(4(0)+10(0))/(4(-2)^3-8(-2))=0$

Hence m=0, that is, the tangent line to the point is a horizontal line that cross the y axis for y=-2. The equation is:

y=(0)x+b = -2

HOPE THIS HELPS!!

In order to find the equation of the tangent line to the curve y²(y² - 4) = x²(x² - 5) at the point (0, -2), we will use the method of implicit differentiation. Here are the steps:

Step 1: Differentiate Each Side of the Given Equation with Respect to x

Applying the chain rule to differentiate y²(y² - 4) with respect to x gives:
2y*y'(y² - 4) + y²*2y*y' = d/dx [y²(y² - 4)]
The chain rule is also applied to differentiate x²(x² - 5) with respect to x, yielding:
2x(x² - 5) + x²*2x = d/dx [x²(x² - 5)]

Step 2: Equate the Two Expressions Found from Step 1 and Solve for y'

2y*y'(y² - 4) + y²*2y*y' = 2x(x² - 5) + x²*2x

This equation can be solved by isolating y' (the derivative of y with respect to x), which represents the slope of the tangent line.

Step 3: Use the Given Point (0, -2) to Find the Slope of the Tangent Line

Substitute x = 0 and y = -2 into the equation found in Step 2 to get the specific value for the slope at the given point.

Step 4: Use the Point-Slope Form of the Line to Write the Equation of the Tangent Line

The point-slope form of the line y - y₁ = m(x - x₁) can be used to write the equation of the tangent line. We substitute for x₁ and y₁ with the coordinates of the given point (0, -2), and m with the slope found from Step 3.

The resulting equation represents the tangent line to the curve at the given point (0, -2). Please note that the full calculation may result in a complex slope due to the nature of the given curve equation. Nonetheless, this process illustrates the application of implicit differentiation and the point-slope form of a line in finding the equation of a tangent line to a curve.

#SPJ3

Determine the measure of < 7
o 53
o 133
o 127
o 47

Answers

Answer:
• 127

Explanation:
How to find 127,
The line is 180°, so you take 53 minus 180.
180-53=127

Hope this helps! Good luck :)

A group of 12 students is deciding whether to go to the science center or the zoo. Science center tickets are 3 for $36.75 and zoo tickets are 4 for $51.How much will a group of 12 students save by choosing the science center?
Enter your answer in the box.

Answers

The group of 12 students will save$6by visiting the science center instead of the Zoo.

Science center fee :

3 tickets = $36.75

Total cost of visiting Science center = (12/3) × 36.75 = $147

Zoo Fee :

4 tickets = $51

Total cost of visiting Zoo = (12/4) × 51 = $153

The difference in the total amount spent :

Total cost of Zoo - Total cost of Science center

$153 - $147 = $6

Therefore, the group will save $6 by visiting the science center.

Learn more : brainly.com/question/18109354

ANSWER:

ExPLANATION:

Step 1:

36.75 × 4 = 147

Step 2:

51 × 3 = 153

Step 3:

153 - 147 = 6

Quick!!! I need to do my homework
Solve: x - 1 < 3

Answers

x < 4

given x - 1 < 3 ( add 1 to both sides )

x < 4

or x ∈ ( - ∞, 4 ) ← in interval notation

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