The density function fy(t) of the random variable Y, where Y = 2x - 2, can be determined by transforming the density function of the random variable X using the given relationship.
To find fy(t), we first need to find the inverse relationship between X and Y. From Y = 2x - 2, we can solve for x:
x = (Y + 2) / 2
Next, we substitute this expression for x in the density function of X, fX(x):
fX(x) = c(3x² + 4)
Substituting (Y + 2) / 2 for x, we have:
fX((Y + 2) / 2) = c[3((Y + 2) / 2)² + 4]
Simplifying the expression:
fX((Y + 2) / 2) = c(3/4)(Y² + 4Y + 4) + 4c
Expanding and simplifying further:
fX((Y + 2) / 2) = (3/4)cY² + 3cY + (3/4)c + 4c
Combining like terms:
fX((Y + 2) / 2) = (3/4)cY² + (12c + 3c)Y + (3/4)c + 4c
Now, we can see that fy(t), the density function of Y, is a quadratic function of Y. The specific coefficients and constants will depend on the values of c.
It is important to note that we need to specify the region where fy(t) is defined. Since fy(t) is derived from fX(x), we need to ensure that the transformation (Y = 2x - 2) is valid for the range of x values where fX(x) is defined.
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verify that the following function is a cumulative distribution function. f(x)={0x<10.51≤x<313≤x round your answers to 1 decimal place (e.g. 98.7).
The probability distribution of X is as follows:P(X = x) = 0 for x < 1P(X = x) = 0 for 1 ≤ x < 10.5P(X = x) = 1 for 10.5 ≤ x < 31P(X = x) = 0 for x ≥ 31.
Given function: f(x)={0x<10.51≤x<313≤xTo verify that the given function is a cumulative distribution function, we have to check the following conditions:1. f(x) is non-negative for all x.2. f(x) is continuous from the right for all x.3. f(x) is a non-decreasing function for all x.4. lim{x → -∞} f(x) = 0 and lim{x → ∞} f(x) = 1. Now, let's verify these conditions one by one.1. f(x) is non-negative for all x. This condition is satisfied, as the given function f(x) is defined only for x ≥ 1, and is non-negative for all x in this domain. Therefore, f(x) is non-negative for all x.2. f(x) is continuous from the right for all x. This condition is also satisfied, as the given function f(x) is defined piecewise as a continuous function for all x. Therefore, f(x) is continuous from the right for all x.3. f(x) is a non-decreasing function for all x. This condition is satisfied, as the given function f(x) is non-decreasing for all x in its domain.4. lim{x → -∞} f(x) = 0 and lim{x → ∞} f(x) = 1.
Using the definition of f(x) for x < 10, we have f(x) = 0 for x < 10. Therefore, lim{x → -∞} f(x) = 0. Using the definition of f(x) for x ≥ 31, we have f(x) = 1 for x ≥ 31. Therefore, lim{x → ∞} f(x) = 1. Hence, all four conditions are satisfied. Therefore, the given function is a cumulative distribution function. To find the probabilities of the intervals, we use the formula: P(a ≤ X ≤ b) = F(b) - F(a)where P(a ≤ X ≤ b) is the probability that X lies between a and b, and F(x) is the cumulative distribution function of X. Furthermore, the probability of the interval (a, b] is: P(a < X ≤ b) = F(b) - F(a)Therefore, the probabilities of the intervals are: P(1 < X ≤ 10.5) = F(10.5) - F(1) = 0 - 0 = 0P(10.5 < X ≤ 31) = F(31) - F(10.5) = 1 - 0 = 1P(X > 31) = F(∞) - F(31) = 1 - 1 = 0Therefore, we have: P(1 < X ≤ 10.5) = 0P(10.5 < X ≤ 31) = 1P(X > 31) = 0
Hence, the probability distribution of X is as follows: P(X = x) = 0 for x < 1P(X = x) = 0 for 1 ≤ x < 10.5P(X = x) = 1 for 10.5 ≤ x < 31P(X = x) = 0 for x ≥ 31. Therefore, the given function is a cumulative distribution function, and the probability distribution of X is as above.
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(a) Find ged(18675, 20112340) (b) Factor both numbers from (b) above. (c) Find the lem of the two numbers from (b) above.
The lem of 18675 and 20112340 is 2^2 * 3^2 * 5^2 * 7 * 83 * 143659.
(a) To find the greatest common divisor (GCD) of 18675 and 20112340, we can use the Euclidean algorithm. The algorithm involves repeatedly dividing the larger number by the smaller number until the remainder becomes zero.
Using the Euclidean algorithm:
20112340 = 1074 * 18675 + 12590
18675 = 1 * 12590 + 6095
12590 = 2 * 6095 + 4000
6095 = 1 * 4000 + 2095
4000 = 1 * 2095 + 1905
2095 = 1 * 1905 + 190
1905 = 10 * 190 + 15
190 = 12 * 15 + 10
15 = 1 * 10 + 5
10 = 2 * 5 + 0
Since the remainder is now zero, the GCD is the last non-zero remainder, which is 5.
Therefore, ged(18675, 20112340) = 5.
(b) To factor the numbers 18675 and 20112340, we can find their prime factorizations.
Prime factorization of 18675:
18675 = 3^2 * 5^2 * 83
Prime factorization of 20112340:
20112340 = 2^2 * 5 * 7 * 143659
(c) To find the least common multiple (LCM) of 18675 and 20112340, we can use the prime factorizations obtained in the previous step.
The LCM is the product of the highest powers of all the prime factors involved.
Prime factors in the LCM:
2^2 * 3^2 * 5^2 * 7 * 83 * 143659
Therefore, the lem of 18675 and 20112340 is 2^2 * 3^2 * 5^2 * 7 * 83 * 143659.
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Given the following data: 46, 47, 110, 56, 71, 109, 63,91, 111,93, 125,78,85, 108,73, 118,70,89,99, 45,73.
Compute the five-number summary and draw the boxplot.
The five-number summary for the given data is as follows: Minimum = 45, First Quartile (Q1) = 71, Median (Q2) = 89, Third Quartile (Q3) = 108, Maximum = 125.
The five-number summary provides key descriptive statistics that summarize the distribution of the data. It consists of the minimum value, the first quartile (Q1), which represents the lower 25% of the data, the median (Q2), which represents the middle value or the 50th percentile, the third quartile (Q3), which represents the upper 25% of the data, and the maximum value.
To draw a boxplot based on this five-number summary, a box is drawn from Q1 to Q3, with a line indicating the median (Q2). Whiskers extend from the box to the minimum and maximum values. Outliers, if present, are represented as individual data points beyond the whiskers.
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I need help figuring out this question
Answer:
no picture
Step-by-step explanation:
The circle radius is 12 cm. Then the circle content is
PLEASE HEEEELP
The following data sets are the math and science test scores, out of 100, for a group of twelve seventh grade students
The interquartile range (IQR) of both the data sets is 8. Create a box plot for each data set Which statement correctly compares
the two data sets?
A. The majority of the math scores are greater than the median of the science scores
B. The majority of the science scores are greater than the median of the math scores
C. The medians of both data sets are equal
D. There is not enough information given to compare the data and medians of the math and science scores
Answer:
The answer and work are in the pdf
Step-by-step explanation:
Answer: A. The majority of the math scores are greater than the median of the science scores
Step-by-step explanation:
I took the test!
identifying the coefficients and constant of a quadratic function consider the quadratic function f(x) = x2 – 5x 6. what are the values of the coefficients and constant in the function? a = b = c =
For the quadratic function f(x) = x^2 - 5x + 6, the values of the coefficients and constant are:
a = 1
b = -5
c = 6.
To identify the coefficients and constant in the quadratic function f(x) = x^2 - 5x + 6, let's examine the standard form of a quadratic equation:
f(x) = ax^2 + bx + c
Comparing this with the given quadratic function, we can determine the values of the coefficients and constant:
a = 1 (coefficient of x^2 term)
b = -5 (coefficient of x term)
c = 6 (constant term)
Therefore, for the quadratic function f(x) = x^2 - 5x + 6, the values of the coefficients and constant are:
a = 1
b = -5
c = 6.
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HELP ASAP PLEASE!!!!
Answer:
Q' = (1, -5)
R' = (3, 1)
S' = (0, 0)
T' = (-2, -3)
Step-by-step explanation:
Look at the numbers of the current vertices and then change the signs of the y-coordinates around. For example, the original Q-coordinate was (1,5) so I changed the 5 to a -5 to reflect across the axis. Changing the y-coordinate sign reflects across the x-axis, while changing the x-coordinate sign reflects across the y-axis.
solve the system using elimination. 4x+5y=2 -2x+2y=8 ( ? , ? )
Answer:
(-2,2)
Step-by-step explanation:
Hi,
4x + 5y = 2
-2x + 2y = 8
To solve using elimination, we can multiply the second equation by 2 to try and get rid of the x. So...
4x + 5y = 2
-4x + 4y = 16
Now, add...
9y = 18
Divide by 9...
y = 2
Now, let's solve for x...
4x + 5(2) = 2
4x + 10 = 2
4x = -8
x = -2
Your solution is, (-2,2)
I hope this helps :)
What is the answer for these this question
HELP ASAP!! In the problem below there is an error in the math. Find the error and write what the error is in complete sentences. You will then work out the problem correctly.
Convert:
35 pounds, 24 ounces=_ ounces
Answer:
Step-by-step explanation:
1 pound = 16 ounces
35 pounds = 560 ounces + 24 ounce = 584ounces
35 pounds,24ounces = 16 ounces
A rabbit is carrying a dominant allele for brown hair (B) and a recessive allele for white hair (b). What is the rabbit's phenotype?
Answer:
B
Step-by-step explanation:
Its dominant because its brown hair.
You are creating a 4-digit pin code. How many choices are there in the following cases? a. With no restriction, b. No digit is repeated, c. No digit is repeated, 2 and 5 must be present.
the number of choices in each case is:
a. With no restriction: 10,000 choices.
b. No digit is repeated: 5,040 choices.
c. No digit is repeated, 2 and 5 must be present: 56 choices.
Let's calculate the number of choices in each case:
a. With no restriction:
For each digit in a 4-digit pin code, we have 10 choices (0-9). Since there are 4 digits in total, the number of choices is 10⁴ = 10,000.
b. No digit is repeated:
For the first digit, we have 10 choices (0-9).
For the second digit, we have 9 choices (any digit except the one chosen for the first digit).
For the third digit, we have 8 choices (any digit except the two chosen for the first and second digits).
For the fourth digit, we have 7 choices (any digit except the three chosen for the first, second, and third digits).
The total number of choices is 10 * 9 * 8 * 7 = 5,040.
c. No digit is repeated, and 2 and 5 must be present:
We have two fixed digits (2 and 5) that must be present in the pin code.
For the first fixed digit (2), we have only 1 choice.
For the second fixed digit (5), we have only 1 choice.
For the remaining two digits, we have 8 choices each (any digit except 2 and 5).
The total number of choices is 1 * 1 * 8 * 7 = 56
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Can someone help me with this. Will Mark brainliest.
Answer:
B ( -1, -8)
Step-by-step explanation:
A ( -7, -6)
midpt (-4, -7)
Equation:
(x + 3, y - 1)
Solve for B:
(-4, -7)
(x + 3, y - 1)
( -1, -8)
ABCD is a quadrilateral that has a four right angle What is the most accurate way to classify this quadrilateral
Answer:
A rectangle
Step-by-step explanation:
A square can be a rectangle but a rectangle can't always be a square.
Does anyone know how to do 3 & 4
Answer:
2.True
3. HGK
4. 17°
hope it helps
does anyone know the answer
Answer:
I think it is A.
Step-by-step explanation:
I hope this helps.
A student is required to solve the initial-value problem as follows:
y ' + 1x+3 y= x2 y-1 , y0= -4.
It is assumed here that x is positive. Then he/she has to find the numerical value of y 2.0, round it off to THREE figures and present the result. A student solved the problem and found that y 2.0 rounded-off to three figures was as follows :
Main Answer: The numerical value of y(2.0) rounded off to three figures is 1.279.
Supporting Explanation:
The student solved the initial-value problem and found that y(2.0) = 1.27977. The question asks to round off the value to three figures. Therefore, we have to keep only the first three digits after the decimal point, which are 279. The next digit after 9 is 7, which means we have to round up the last digit. Thus, the rounded off value of y(2.0) is 1.279.
The initial-value problem is a differential equation that has an initial condition given for a specific value of the independent variable. In this case, the initial condition is y(1) = 2. The solution of the initial-value problem gives the value of y for other values of x. Here, we are required to find the value of y for x = 2.0.
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A fifth-grade class is earning points for a pizza party by reading books.
For every book they read, they earn 6 points. Complete the table, where b represents the number of books read. How many points will they earn if b = 24?
Answer:
144
Step-by-step explanation:
24 books at 6 points each would be 24 x 6 which equals 144
Answer:
They'll have 144 points if they read 24 books.
Step-by-step explanation:
6 x 24 = 144
Please help me.
Please simplify it and group it in like terms.
3a+6+2a-4+a-2=
Answer:
6a
Step-by-step explanation:
Answer:
6a
Step-by-step explanation:
3a+2a+a= 6a
6-4-2=0
6a+0=6a
A local pet groomer accepts walk-in customers. From experience, the groomer has determined that the probability that a walk-in customer will get a full-service grooming, which includes a bath and nail trimming, is 0.71. The probability that a walk-in customer will get a haircut for their pet is 0.42. The probability that customers who get the full-service grooming will also ask for a haircut is 0.28. What is the probability that a walk-in customer will ask for both a full-service grooming and a haircut?
0.12
0.20
0.28
0.30
Answer:
0.28
Step-by-step explanation:
Answer:
0.20
Step-by-step explanation:
i got it right on edge 2022
15% of $9.00 is $
I need help!!
Answer:
$ 1.35
Step-by-step explanation:
9 times 0.15 is 1.35
Find the volume of the cylinder. Round your answer to the
nearest tenth.
WILL GIVE BRAINLY
Answer:
7 cm
Step-by-step explanation:
10 mm = 1cm
All you need to do is add 10mm + 6cm.
10mm = 1cm
So, 6cm + 1cm.
Therefore, it equals to 7cm.
Answer:
471.2 cm cubed
Step-by-step explanation:
The formula for the volume of a cylinder is:
π*radius squared*height
The diameter is the distance across the circle.
10 mm is the same as 1 cm
The radius is half of the diameter.
1/2=.5
Radius=.5 cm
Height=6 cm
Plug the numbers in.
.5 squared is .25
π*(.25)(6 cm)
Volume=4.71
Rounded to the nearest tenth:
Volume=4.7 cm cubed
PLEASE HELP FOR BRAINLIEST! The sum of two numbers is 4 and the difference of their squares is 64. Find the two numbers.
10 and -6
.....................................................
Approximately what percentage of hardcover books sold were nonfiction?
Answer:
B
Step-by-step explanation:
Kim's fish is 10 inches long.
Sam's fish is 3 inches long.
How many inches shorter is Sam's fish?
Answer:
7
Step-by-step explanation:
Answer:
Sam's is 7in shorter
Step-by-step explanation:
[tex]10-3=7[/tex]
A dartboard has 20 equally divided wedges, and you are awarded the number of points in the section your dart lands in. If you are equally likely to land in any wedge, what is the probability you will score 10, 11, or 12 points?
Answer: 10 points
Step-by-step explanation:
Find the square root of -i
that graphs in the second quadrant.
The square root of -i that graphs in the second quadrant,
⇒ z = (1/2)((√(2))(cos(135°) + i sin(135°))
To find the square root of -i,
we can start by writing -i in polar form.
⇒ i = 1(cos(270°) + i sin(270°))
Now, we can find the square root by taking the square root of the magnitude and dividing the angle by 2.
⇒ √(-i) = √(1) [cos(270°/2) + i sin(270°/2)]
⇒ [tex](1)^{(1/2)}[/tex] [cos(135°) + i sin(135°)]
⇒ (1/2)(√(2)) [cos(135°) + i sin(135°)]
⇒ (1/2)(√(2)) (-√(2)/2 + i(√(2))/2)
⇒ -1/2 + ((√t(2)/2)i
Therefore,
The square root of -i that graphs in the second quadrant in the form of
z = r(cosθ + i sinθ)
Hence,
z = (1/2)((√(2))(cos(135°) + i sin(135°)).
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statistics are used to: a. ask questions b. make estimates of population parameters c. form a basis for analysis d. theoretically specify grouping of study elements
Statistics are used to make estimates of population parameters. Therefore, the correct option is B.
Statistics are used for various purposes in data analysis. One important application of statistics is to make estimates of population parameters. Population parameters are characteristics or measures that describe an entire population. However, it is often impractical or impossible to collect data from the entire population, so statistics provide methods for estimating these parameters based on a sample of the population.
By collecting and analyzing data from a sample, statisticians can make inferences and draw conclusions about the larger population. These estimates help researchers understand the characteristics, patterns, and relationships within the population.
Additionally, statistics form the basis for analysis in many fields, including scientific research, business, social sciences, and more. They provide tools and techniques to summarize, interpret, and draw meaningful insights from data, enabling researchers and decision-makers to make informed choices and draw valid conclusions from their observations and experiments.
Therefore, the correct choice is option b. Statistics play a crucial role in estimating population parameters and providing insights for analysis and decision-making.
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