Let Z ~ N(0, 1) and X ~ N(μ σ2) This means that Z is a standard normal random variable with mean 0 and variance 1 while X is a normal random variable with mean μ and variance σ2. Calculate E(Z3) (this is the third moment of Z)
Answers
Let's calculate E(Z^3), which is the third moment of Z, given that Z follows a standard normal distribution N(0, 1) and X follows a normal distribution N(μ, σ^2).
First, recall that the third moment of a random variable, E(Z^3), represents the expected value of the cube of Z. In this case, Z is a standard normal random variable, which has a symmetric probability density function (PDF) about the mean 0.
To calculate E(Z^3), we can use the formula:
E(Z^3) = ∫ z^3 * f(z) dz
where f(z) is the PDF of the standard normal distribution, and the integral is taken from negative infinity to positive infinity.
Since the PDF of Z is symmetric about the mean 0, the values of z^3 * f(z) will be positive for positive z values and negative for negative z values. These positive and negative values will cancel each other out when integrating over the entire range of Z, resulting in E(Z^3) = 0.
In summary, the third moment of Z, E(Z^3), for a standard normal random variable Z is 0 due to the symmetry of the PDF about the mean 0.
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Related Questions
in a local election, votes were cast for mr. dyer, ms. frau, and mr. borak in the ratio of 4:3:2. if there were no other candidates and none of the 2,700 voters cast more than one vote, how many votes did mr. dyer receive?
Answers
To calculate the number of votes that Mr. Dyer received, we need to multiply the ratio with the total votes. Mr. Dyer received 1,080 votes.
Ratio of votes = 4:3:2
Total votes = 4 + 3 + 2 = 9
Total votes cast = 2,700
Mr. Dyer's votes = (4/9) x 2,700 = 1,080 votes
The ratio of votes cast for Mr. Dyer, Ms. Frau and Mr. Borak was 4:3:2 respectively. This means that for every 9 votes cast, 4 votes were for Mr. Dyer, 3 votes were for Ms. Frau and 2 votes were for Mr. Borak. Since none of the 2,700 voters cast more than one vote, the total votes cast for each candidate would be 2,700. To calculate the number of votes that Mr. Dyer received, we need to multiply the ratio with the total votes. Therefore, Mr. Dyer received 1,080 votes (4/9 x 2,700).
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Which of the following inequalities is graphed on the coordinate plane? A.y≤-2x=+1
Answers
Answer:
y≤-2x=+1
Step-by-step explanation:
this will definitely on coordinate plan.
Kindly completed your question as it seem unfinished
write an algebraic expression for each verbal expression. four more than the product of six and a number q
Answers
A farmer wants to fence an area of 6 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. Let y represent the length (in feet) of a side perpendicular to the dividing fence, and let x represent the length (in feet) of a side parallel to the dividing fence. Let F represent the length of fencing in feet. Write an equation that represents F in terms of the variable x.
Answers
If the rectangular field has notional sides X and y then it has area
A(x) =xy { =6•10^6 sq ft }
The length of fencing required, if
x
is the letter that was arbitrarily assigned to the side to which the dividing fence runs parallel, is:l (x) = 3x +2y
It matters not that the farmer wishes to divide the area into 2 exact smaller areas.
Assuming the cost of the fencing is proportional to the length of fencing required, then
C(x)=a L (x)
To optimise cost, using the Lagrange Multiplier
λ
, with the area constraint :
So the farmer minimises the cost by fencing-off in the ratio 2:3, either-way
The relationship between variable F and x is 2x + 12000000/x
Let y represent the length (in feet) of a side perpendicular to the dividing fence, and let x represent the length (in feet) of a side parallel to the dividing fence.
Let F represent the length of fencing in feet.
Area of fencing = 6000000 ft²
Area of fencing = x * (y + y) = x * 2y
Area of fencing = 2xy
6000000=2xy
xy = 3000000
y = 3000000/x
The perimeter is:
F = x + y + y + x + y + y
F = 2x + 4y
F = 2x + 4(3000000/x)
F = 2x + 12000000/x
Therefore the relationship between variable F and x is 2x + 12000000/x
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The results from a study using a One-Way ANOVA indicate that there are significant differences between conditions, F(4,55) = 6.17, p<.05, eta² = .19 In Blank 1: How many treatment conditions were compared in this study? In Blank 2: How many individuals participated in the entire study Blank # 1 A Blank #2
Answers
Blank 1: In this study, 5 treatment conditions were compared
Blank 2: There were 60 individuals who participated in the entire study
The Independent Samples t Test is extended by the One-way ANOVA (In independent samples t test used to compare the means between two independent groups, whereas in one-way ANOVA, means are compared among three or more independent groups).
Whereas a two-way ANOVA employs two independent variables, a one-way ANOVA just uses one.
Example of One-Way ANOVA You want to examine how three different fertilizer combinations affect crop yield as an agricultural researcher.
ANOVA comes in two primary flavours: one-way (also known as unidirectional) and two-way. ANOVA can also take several forms.
The mean of a quantitative variable is estimated using a two-way ANOVA in relation to the values of two categorical variables
Blank 1: In this study, 5 treatment conditions were compared (the number of conditions is one more than the first number in the F-statistic, which is 4).
Blank 2: There were 60 individuals who participated in the entire study (you can calculate this by adding the two numbers in the F-statistic and then adding 1,
so 4 + 55 + 1 = 60).
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Christina is doing an obstacle course in gym class. First, she runs 100 feet and jumps over a hurdle. Then, she crawls through a 20-foot tunnel. Finally, she dribbles a soccer ball 60 feet to the finish line. How many yards long is the obstacle course?
Answers
Answer:
60 yards
Step-by-step explanation:
100 feet + 20 feet + 60 feet = 180 feet
180 feet = 60 yards (there are 3 feet in 1 yard)
Gabrielle designs bow ties for a local boutique store. The store manager counted the ties currently on display, tracking them by material and shape. Butterfly Batwing Cotton 10 11 Suede 8 13 What is the probability that a randomly selected bow tie is made of suede and is shaped like a butterf Simplify any fractions.
Answers
The table shows the types of bow ties currently on display and the material they are made of.
You have to determine the join probability of that bow tie being made of Suede (S) and its shape is like a butterfly (F).
If you display all possible combinations of the shapes and materials of the bowties you'll get the following combinations:
If f(x) = 3x – 1 and g(x) = x^2 + 4, find the (gºf)(x).
Answers
Answer: 9x²-6x+5
Step-by-step explanation:
To find (gοf)(x), you want to plug f(x) into g(x). It is the same as g(f(x)).
g(f(x))=(3x-1)²+4 [distribute by FOIL]
g(f(x))=9x²-6x+1+4 [combine like terms]
g(f(x))=9x²-6x+5
Now, we know that (gοf)(x)=9x²-6x+5.
What is 5m^2+9n^3-mn^2+2m^3
Answers
The given expression is:
5m^2 + 9n^3 - mn^2 + 2m^3
This expression is a polynomial. The correct answer is option c.
It consists of four terms:
5m^2: This term is a monomial with a coefficient of 5 and a single variable, m, raised to the power of 2.
9n^3: This term is a monomial with a coefficient of 9 and a single variable, n, raised to the power of 3.
-mn^2: This term is a monomial with a coefficient of -1 and two variables, m raised to the power of 1 and n raised to the power of 2.
2m^3: This term is a monomial with a coefficient of 2 and a single variable, m, raised to the power of 3.
Therefore, The expression 5m^2 + 9n^3 - mn^2 + 2m^3 is a ploynomial. which is option c
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The probable question may be:
What is 5m^2+9n^3-mn^2+2m^3
choose the correct answer
a) monomial
b) binomial
c) polynomial
can someone whos good at geometry pleaseeee help me with my homework???????
Answers
I'm good at geomotry what do u need help with?
Amir drove from Jerusalem to the lowest place on Earth, the Dead Sea.
His altitude relative to sea level (in meters) as a function of time (in minutes) is graphed.
How long did it take Amir to reach sea level?
Answers
In order to solve this problem, we need to begin by examining the graph of Amir's altitude relative to sea level. We can see that the graph starts at an altitude of 700 meters and ends at an altitude of 400 meters.
We can also see that the slope of the graph is negative, which means that the altitude is decreasing over time. This means that it will take Amir some amount of time to reach sea level (which is 0 meters).
To calculate how long it took Amir to reach sea level, we can use the following equation:
Time = (Altitude Final - Altitude Initial) / (Rate of Change)
In this equation, the Rate of Change is the slope of the graph, which can be determined by examining the graph.
Plugging in our values, we get:
Time = (400 - 700) / (-6) = 100 / (-6) = -16.67 minutes
Therefore, it took Amir 16.67 minutes to reach sea level.
Solve.
12.25 = 2.5 =
4.9
4.5
6.5
0.49
Answers
12.25 divided by 2.5= 4.9
Hope this helps
Have a great day/night
For i =√√1, what is the value of
(2+3i)(5-7i)?
Answers
result is 31+i in where 31 is real part and i is complex part as given i= √-1 and i²= -1
What is called complex number?In mathematics complex number is an element which has two parts one is called real part and the remaining is termed as imaginary part. An example is 41+6i
here, 41 is real part, 6i is imaginary part
What is the system we use for complex number?A real number cannot be added or subtracted with an imaginary number, but a real number can be multiplied or divided with an imaginary number.
We are given, (2+3i) (5-7i)
at first, we expand it by removing parenthesis
2x5-2x7i+3ix5-3ix7i
10-14i+15i-21i²
now like term is added
10+i+21 as we are given i²= -1
31+i
hence, we get 31+i
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The graph of f(x) =7x is reflected across the x-axis. write a function g(x) to describe the new graph. G(x)=___
Answers
To reflect a function across the x axis, we just stick a negative in front. This will make all point's y coordinates to go from positive to negative or vice versa. If the original function already has a negative out front, then remove it.
The Ratio of two numbers is 3/5, and their sum is 104. What are the 2 numbers?
Answers
Answer:
39 and 65
Step-by-step explanation:
the ratio of the two numbers is 3 : 5
sum the parts of the ratio, 3 + 5 = 8 parts
divide the sum by 8 to find the value of one part of the ratio
104 ÷ 8 = 13 ← value of 1 part of the ratio , then
3 parts = 3 × 13 = 39
5 parts = 5 × 13 = 65
the two numbers are 39 and 65
The projected worth (in millions of dollars) of a large company is modeled by the equation w = 241(1.06) t. the variable t represents the number of years since 2000. what is the projected annual percent of growth, and what should the company be worth in 2011?
Answers
Answer:
6%- 457 Million
Step-by-step explanation:
w=241(1.06)^11=457 million
statistics include numerical facts, ratios, percentages, and more complex ways of analyzing and comparing numerical data.
Answers
Determine cause-and-effect relationships between variables (regression analysis)
Statistics are methods used to collect, analyze, interpret, present, and organize data.
It includes numerical facts, ratios, percentages, and more complex ways of analyzing and comparing numerical data. Statistics is a discipline that concerns itself with designing and developing methods for collecting, analyzing, and interpreting data.
The aim of statistics is to summarize and present data in a meaningful and useful way. It is an important tool in almost every field of study, from business and economics to health care and science.
Statistics is used to:
Describe data (descriptive statistics)Infer information from samples of data to a larger population (inferential statistics)
Analyze and test hypotheses about relationships between variables (hypothesis testing)
Examine the associations between variables (correlation analysis)
Determine cause-and-effect relationships between variables (regression analysis)
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When an object that is denser than water is dropped into a vessel of water, the object
sinks to the bottom and displaces water, making the water level rise in the vessel.
The volume of water displaced is equal to the volume of the submerged object. A
60cm diameter steel ball is dropped into a cylindrical vessel of water, sinks to the
bottom and is fully submerged. Before dropping the ball in, the water is 125 cm deep
and after the ball is dropped in, the water level rises 5cm. Find the radius of the
cylindrical vessel.
125 cml
Answers
The radius of the cylindrical vessel is , 29.4 cm.
Now, For the volume of water displaced by the steel ball. We can use the formula:
V = Ah
Where V is the volume of water displaced, A is the cross-sectional area of the submerged portion of the steel ball, and h is the rise in water level.
And, The cross-sectional area of the steel ball can be found using the formula for the area of a circle:
A = πr²
where r is the radius of the steel ball.
Here, The rise in water level is, 5 cm.
So we have:
V = πr²h
We can also find the volume of the steel ball using the formula:
V = (4/3)πr³
We know that the diameter of the steel ball is 60 cm, so the radius is 30 cm.
The volume of the steel ball is:
V = (4/3)π(30)³
V = 113,097.34 cubic centimeters
Now we can find the volume of water displaced by the steel ball:
V = πr²h
V = 113,097.34 cubic centimeters
We know that the rise in water level is 5 cm and the initial depth of the water is 125 cm,
Hence, the final depth of the water after the steel ball is dropped in is,
125 + 5 = 130 cm.
Now, Let us assume that, the radius of the cylindrical vessel r.
The volume of water in the vessel can be found using the formula:
V = πr²h
where h is the height of the water in the vessel.
We know that the initial height of the water is 125 cm, and the final height is 130 cm, so the height of the water displaced by the steel ball is 5 cm.
We can now set up an equation to solve for r:
πr²(125) + πr²(5) = 113,097.34
Simplifying:
πr²(130) = 113,097.34
r² = 864.96
r = 29.4 cm
Therefore, the radius of the cylindrical vessel is 29.4 cm.
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line c and d are perpendicular. the slope of line c is -2/3. which equation is true?
Answers
The correct expression for the slopes of two perpendicular lines are:
-2/3 . slope of d = -1
Explain about the slope of line:The difference between the change in y-values and the change in x-values is known as the slope of a line. This figure represents the slope of a line.
A quantity called the slope of a line is used to quantify how steep a line is. This number may be zero, positive, or negative. Moreover, it may be unreasonable or rational.
At a 90 degree angle, perpendicular lines collide. There are as many perpendicular lines to a given line as there are parallel lines. Simply said, they will cross the indicated line at various points.Two perpendicular lines' slopes are connected. Each is the reciprocal opposite sign of the other.For the two given perpendicular lines with slope c and d.
slope of c = -2/3
Then,
slope of c . slope of d = - 1
-2/3 . slope of d = - 1
Thus, the correct expression for the slopes of two perpendicular lines are: -2/3 . slope of d = -1
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Answer:
3/2
Step-by-step explanation:
If a line is perpendicular to the other it's slope is the inverse reciprocal of the other slope
PLEASE SIMPLIFY THIS
Answers
Answer:
15y / 8
Step-by-step explanation:
Multiplying by 2 to get the common denominator.
3y / 4 * 2 = 6y / 8
Combine like terms.
6y / 8 + 9y / 8
Final Answer:
15y / 8
Solve for x. Round to the nearest tenth, if necessary.
Answers
So the answer is 1.3 after rounding to 10.
In a litter of 7 kittens, each kitten weighs less than 3.5 ounces. Find and graph all the possible combined weights of the kittens.
Answers
Answer:
Step-by-step explanation:
24.5 just multiply hope that helpss
The local gym is charging a flat fee of $20 per month to be a member. Each time you go to the gym you pay $2 for a bottled water. What equation would represent how much you pay in total for the month if x is equal to the number of times you go to the gym?
multichoice
y=2x+10 y=22x
y=20x+2 y=2x+20
Answers
Answer:
y = 2x +20
Step-by-step explanation:
Times at gym = x
You get a waterbottle every x times = 2x.
The equation represents total in a month so the flat fee is not included.
5 times the sum of a number and -2 equals 30
Answers
Answer: 5(x+-2) = 30
Step-by-step explanation:
Answer:
x=8
Step-by-step explanation:
5(x+(-2))=30
5x-10=30
+10 +10
5x=40
/5. /5
x=8
Hopes this helps please mark brainliest
The second highest point measured above sea level is the summit of
Kangchenjunga which is 8,586m above sea level and the lowest point is
challenger deep at the bottom of Mariana Trench which is 10,911 m below
the sea level. What is the vertical distance between these two points? Collect
some more information about these two points and present them withimages.
Answers
Answer:
19497 m
Step-by-step explanation:
The vertical distance between the given points is:
10911 + 8586 = 19497 mAnswer:
19,497m
Step-by-step explanation:
8,856-(-10,911)
=8856+10,911
=19,497m
Will give brainliest to the correct answer!:)
What is the value of the logarithm?
In(81)
Round the answer to the nearest ten thousandth.
Answers
Answer: log81 = 1/4
Step-by-step explanation:
Log81^3
81^x = 3
The common base is 3, so
(3^4)^x=3
3^4x = 3^1
4x = 1
x= 1/4
Find an ordered pair (x,y) that is a solution to the equation. 3x-y=8
Answers
Answer:
(2,-2)
Step-by-step explanation:
\(3x-y =3(2) -(-2)= 6 +2 = 8\)
A number increased by 4 is less than 19.
Answers
Answer:
23 is the answer u understand
simplify (18+t)(-3)+9
Answers
Answer:
-3t-45
Step-by-step explanation:
(18+t)(-3)+9
18x-3-3t+9
-54-3t+9
-3t-54+9
-3t-45
Given m||n, find the value of x.
Plz help :)
Answers
Answer:
x is = 25° by complimentary angles