Question

(a) Compute dW4(t) and then write W4(t) as the sum of an ordinary (Riemann) integral and an Ito integral. (b) Take expectations on both sides of the formula you obtained in part (a) and derive a formula for E(W4(t)). (C) Use the method of (a) and (b) to derive a formula for E(Wº(t)). (d) Calculate the variance Var (+W3(T) DW (t)).

Answer #1

For the function given below, find a formula for the Riemann
sum obtained by dividing the interval [a,b] into n equal
subintervals and using the right-hand endpoint for each
c Subscript kck.
Then take a limit of this sum as
n right arrow infinityn → ∞
to calculate the area under the curve over [a,b].
f(x)equals=44x
over the interval
[00,44].
Find a formula for the Riemann sum.

5. A problem to connect the Riemann sum and the Fundamental
Theorem of Calculus:
(a) Evaluate the Riemann sum for f(x) = x 3 + 2 for 0 ≤ x ≤ 3
with five subintervals, taking the sample points to be right
endpoints.
(b) Use the formal definition of a definite integral with right
endpoints to calculate the value of the integral. Z 3 0 (x 3 + 2)
dx.
Note: This is the definition with limn→∞ Xn i=1 f(xi)∆x...

Use a graphing calculator Riemann Sum (found here) to
find the following Riemann sums.
f(x) =
2/x
from a = 1 to b =
5
(a) Calculate the Riemann sum for the function for the following
values of n: 10, 100, and 1000. Use left, right, and
midpoint rectangles, making a table of the answers, rounded to
three decimal places.
n
Left
Midpoint
Right
10
100
1000
(b) Find the exact value of the area under the curve by
evaluating an appropriate definite...

f(x) =
square root x
from a = 4 to b =
9
(a) Calculate the Riemann sum for the function for the following
values of n: 10, 100, and 1000. Use left, right, and
midpoint rectangles, making a table of the answers, rounded to
three decimal places.
n
Left
Midpoint
Right
10
100
1000
(b) Find the exact value of the area under the curve by
evaluating an appropriate definite integral using the Fundamental
Theorem. The values of the Riemann sums from...

a. Roll a dice, X=the number obtained. Calculate E(X), Var(X).
Use two expressions to calculate variance.
b. Two fair dice are tossed, and the face on each die is
observed. Y=sum of the numbers obtained in 2 rolls of a dice.
Calculate E(Y), Var(Y).
c. Roll the dice 3 times, Z=sum of the numbers obtained in 3
rolls of a dice. Calculate E(Z), Var(Z) from the result of part a
and b.

In a small-scale regression study, we collected data on the
number of children in a family Xi and the number of
hours per week spent shopping Yi. The following data
were obtained:
i
1
2
3
4
5
6
Xi
2
6
3
1
1
9
Yi
13
17
12
12
9
22
Assume we performed a simple linear regression of Yi
on Xi, i.e. E(Yi) = ?0 +
?1Xi
(a) By hand compute X?X, X?Y, (X?X)-1, b,
Y^(means Y-hat),...

answering the question(s), make sure to write down the following
7 steps.
Step 1: Establish null and alternate hypotheses State the null
and alternative hypothesis (as a sentence and formula).
Step 2: Calculate the degrees of freedom
Step 3: Calculate t critical using critical t – table
Step 4: Calculate the Sum of Square deviation (SSD)
Step 5: Calculate t obtained
Step 6: Specify the critical value and the obtained value on a
t-distribution curve
Step 7: Decision and Conclusion...

Problem #1 Confidence Interval for Means using the t and
z Distribution. Psychologists studied
the percent tip at a restaurant when a message indicating that the
next day’s weather would be nice was written on the bill. Here are
tips from a random sample of patrons who received such a bill,
measured in percent of the total bill:
20.8 18.7
19.9 20.6
21.9 23.4
22.8 24.9
22.2 20.3
24.9 22.3
27.0 20.4
22.2 24.0
21.1 22.1
22.0 22.7
Open an...

Question 3
(a) [10 marks] FAEN102 students must attend t hours, where t ∈
[0,H], of lectures and pass two quizzes to be in good standing for
the end of semester examination. The number of students who
attended between t1 and t2 hours of lectures is de- scribed by the
integral
? t2
20t2 dt, 0≤t1 <t2 ≤H.
t1
As a result of COVID-19, some students attended less than H2
hours of lectures before the university was closed down and...

Independent-Samples t-Test
In a research project, researchers track the health and
cognitive functions of the elderly in the community. To examine any
possible gender differences in their sample, they want to see if
the females and the males differ significantly on the education
level (number of years of formal schooling). The researchers are
not predicting any direction in the possible gender differences so
the hypotheses should be non-directional. They would like to run a
two-tailed test with α = .10....

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