if u is uniformly distributed on (0 1) find the distribution of y=-log(u)
Answers
the distribution of y=-log(u) is an exponential distribution with parameter 1.
To find the distribution of y=-log(u), we need to first find the cumulative distribution function (CDF) of y.
Let F(y) be the CDF of y. Then,
F(y) = P(y ≤ y') = P(-log(u) ≤ y') = P(u ≥ e^(-y'))
where y' is any real number.
Since u is uniformly distributed on (0, 1), P(u ≥ e^(-y')) = 1 - P(u < e^(-y')) = 1 - e^(-y')
Therefore,
F(y) = 1 - e^(-y)
This is the CDF of y. To find the probability density function (PDF) of y, we differentiate F(y) with respect to y:
f(y) = F'(y) = d/dy (1 - e^(-y)) = e^(-y)
If U is uniformly distributed on the interval (0, 1), we can find the distribution of Y = -log(U) by determining the probability density function (pdf) of Y. To do this, we'll use the transformation technique.
1. First, we find the inverse transformation: U = e^(-Y).
2. Next, compute the derivative of U with respect to Y: dU/dY = -e^(-Y).
3. Take the absolute value of the derivative: |dU/dY| = e^(-Y).
4. Finally, substitute this value into the pdf of U (which is 1 for a uniform distribution on (0, 1)) and multiply by the Jacobian, which is the absolute value of the derivative of the transformation.
The pdf of Y, denoted as f_Y(y), is given by:
f_Y(y) = f_U(u) * |dU/dY| = 1 * e^(-Y) = e^(-Y), for Y > 0.
This implies that Y follows an exponential distribution with a rate parameter of 1.
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Related Questions
Nine more than thirty divided by ten. Numerical expression
Answers
The numerical expression for the verbal expression eighteen more than five is (9 + 30) / 10.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now the given verbal expression is,
Nine more than thirty divided by ten
Now converting them into numerical expression,
nine = 9
thirty = 30
∵ more than is addition i.e. +
∴ Nine more than thirty = 9 + 30
ten = 10
So, the numerical expression is given as,
Nine more than thirty divided by ten = (9 + 30) / 10
Thus, the numerical expression for the verbal expression eighteen more than five is (9 + 30) / 10.
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An air temperature of 30°C is equal to
1. -1°F
2. 68°F
3. 83°F
4. 86°F
Answers
Answer:
86 degrees fahrenheit
Step-by-step explanation:
(30°C × 9/5) + 32 = 86°F
I’m not the best but hope this helps!
What is the vertex of the quadratic function f(x) = (x-8)(x - 2)?
Answers
Answer:
The vertex is at (5, -9)
Step-by-step explanation:
The vertex is halfway between the zeros
f(x) = (x-8)(x - 2)
0 = (x-8)(x - 2)
x=8 and x=2 are the two zeros
(8+2)/2 = 10/2 = 5
The x coordinate is at 5
The y coordinate is found by substituting the x coordinate into the function
f(5) = (5-8)(5 - 2) = -3 (3) = -9
The vertex is at (5, -9)
Write 6^4÷√6 as a single power of 6.
Answers
\(~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ 6^4\div \sqrt{6}\implies \cfrac{6^4}{\sqrt{6}}\implies \cfrac{6^4}{6^{\frac{1}{2}}}\implies 6^4\cdot 6^{-\frac{1}{2}} \\\\\\ 6^{4-\frac{1}{2}}\implies 6^{\frac{8-1}{2}}\implies 6^{\frac{7}{2}}\)
there are (36)2⋅ 30 candies in a store. what is the total number of candies in the store? (5 points) group of answer choices 312 33 38 34 next
Answers
The total number of candies in the store is 312. It is obtained by using the concept of exponent and power on the given problem.
What is an Exponent?
The number of times a quantity is multiplied by itself is referred to as an exponent or power of the given quantity. For eg: 25, where 5 is an exponent or power of 2 and 2 is called the base of exponent 5. Any quantity raised to the power 0 always returns 1 as result.
Calculation of the total number of candies in the store
(36)2 * 30
Using the properties of an exponent, we have
A number with an exponent of 0 always gives 1
(36)2 * 1
(3)6×2 * 1
312 * 1
312
Thus, the total number of candies in the store is 312.
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Matt has 2/3 yard of fishing line. He uses 3/8 to make fishing knots. Shade the model to show the amount of line that Matt uses to make fishing knots?
Answers
Answer:
1/4 yards was to make fishing knot
Step-by-step explanation:
Given that :
Yards of fishing line = 2/3
Fraction used to make fishing knot = 3/8
Amount of yards used to make fishing knot;
3/8 of the number of yards was used to make fishing knot.
(3/8) of 2/3)
(3/ 8) * (2 /3)
6 / 24
= 1 / 4 yards
A coin is flipped eight times where each flip comes up either heads or tails. The outcome is the string of 8 heads/tails that is produced. How many possible outcomes
Answers
There are 256 possible outcomes for the string of 8 heads/tails that can be produced when flipping a coin eight times.
When a coin is flipped eight times, there are two possible outcomes for each individual flip: heads or tails.
Since each flip has two possibilities, the total number of possible outcomes for eight flips can be calculated by multiplying the number of possibilities for each flip together.
Therefore, the number of possible outcomes for eight coin flips is:
2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 2^8 = 256
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Help!! I believe I need to find the L and W of browns rectangle to make macdonalds equation but I’m stuck there and need to answer the whole thing for 11
Answers
Answer:
W man's W life W parents W pet W grand parents
4. [10 pts] Suppose that you generate a 12-character password by selecting each character independently and uniformly at random from {a,b,..., z}U {A, B, ..., Z} U {0, 1, ..., 9}. (a) What is the probability that exactly 6 of the characters are digits? (b) What is the expected number of digits in a password? (c) What is the variance of the number of digits in a password?
Answers
(a) The probability that exactly 6 of the characters in the password are digits is approximately 0.2412.
(b) The expected number of digits in a password is approximately 1.935.
(c) The variance of the number of digits in a password is approximately 0.303.
(a) To compute the likelihood that precisely 6 of the characters in a 12-character secret word are digits, we can utilize the binomial likelihood recipe. Give X be the quantity of digits access the secret phrase. We need to track down P(X = 6).
The likelihood of choosing a digit is 10/62 since there are 10 digits and a sum of 62 characters to look over (26 lowercase letters + 26 capitalized letters + 10 digits).
Utilizing the binomial likelihood equation, P(X = 6) = C(12, 6) * \((10/62)^_6\) * \((52/62)^_6,\) where C(12, 6) is the quantity of mixes of picking 6 things out of 12.
Ascertaining this articulation, we track down P(X = 6) ≈ 0.2412.
(b) The normal number of digits in a secret phrase can be found by duplicating the likelihood of having a digit in each position (10/62) by the complete number of positions (12): E(X) = (10/62) * 12 = 1.935.
Consequently, the normal number of digits in a secret phrase is roughly 1.935.
(c) To work out the fluctuation of the quantity of digits in a secret word, we can utilize the recipe Var(X) = \(E(X^2) - (E(X))^2\).
\(E(X^2)\)= (10/62) * 12 * (11/62) * 11 + (52/62) * 12 * (51/62) * 11 ≈ 2.482.
Var(X) =\(E(X^2) - (E(X))^2\) = 2.482 - \((1.935)^_2\) ≈ 0.303.
Consequently, the fluctuation of the quantity of digits in a secret word is roughly 0.303.
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pls help with these, at least up to finishing question 2 or Question 3b
Answers
Answer:
For question 3b the answer is no because the common difference is 4
Step-by-step explanation:
6,10,14,18,22,26,30,34
It will be 34 not 33
SOMEONE ANSWER QUICK!!
Steven bought 4 pizzas to share with his family. Together, they ate 2 7/12 pizzas on Friday and another 2/3 of a pizza on Saturday. How much pizza is left??
Answers
Answer:
3/4 pizza is left. If you want an explanation, ask me ;>
3/4
Explanation:
You have 4 and you eat 2 7/12. Leaving you 1 5/12. Then you eat 8/12 more leaving you 9/12 which simplifies to 3/4
The average number of students per class at a middle school
is 22. There are t teachers in the school, and there is one
teacher for each class. Which equation represents the total
number of students, s, in the school?
Answers
Answer:
s = 22t or \(\frac{t}{s} = \frac{1}{22}\), when s is students and t is teachers.
Step-by-step explanation:
I. Given t = teacher, s = student
When 1 teacher per 22 students so...
s = 22t
If there're 10 teachers
s = 22(10)
= 220 or \(\frac{t}{s} = \frac{1}{22}\)
Hope that help :)
“which sport do you prefer soccer or basketball is”that biased or unbiased question
Answers
Answer: both
Step-by-step explanation:
(-9, 19), (10, 16)
Find the slope of the line through each pair of points
Answers
Answer:
-3/19
Step-by-step explanation:
slope = rise/run = (y1 - y2) / (x1 - x2)
s = (19 - 16) / (-9 -10)
s = 3/-19 = -3/19
Definition of Variable and Constant with examples!
Spam free answers required!
Answers
Answer:
\(\large\boxed{\boxed{\boxed{\mathfrak{variable}}}}\)
Variable is a symbol that represents a quantity in a mathematical expression, as used in many sciences. Variable (research), a logical set of attributes. Variable star, a type of astronomical star.
\(\large\boxed{\boxed{\boxed{\mathfrak{constant}}}}\)
A constant, sometimes also called a "mathematical constant," is any well-defined real number which is significantly interesting in some way. A function, equation, etc., is said to "be constant" (or be a constant function) if it always assumes the same value independent of how its parameters are varied.
If the ratio of the sides of a triangle are 13:14: 15 and its perimeter is 84 cm, find
the area of the triangle.
Answers
Answer:
26, 28, 30
Step-by-step explanation:
perimeter of the base ratio triangle is 42
42x2=84
since you are given ratio, multiply individual values by 2
Answer is achieved
in this activity, you will connect doing business with using the tools of algebra. You've seen a lot of scenarios in which people business use algebra to ensure or monitor their success, including maximizing profit, reaching revenue goals, and calculating the consequences of price increases. Imagine that you're involved in a business venture that could benefit from algebraic expressions and calculations . If you've been involved in such a business , recall what that experience entailed Write a paragraph describing the business venture and what kind of algebra or other calculations and formulas might help someone in that endeavor . Also include ways in which the business might operate differently with those tools than without them.
Answers
Answer: check explanation for the solution
Step-by-step explanation:
A business that offers services to people by providing many amusement and fun with gate fees
The algebraic equations to be used is the general linear equation
Y = MX + C
Where
Y = total income or money realised
M = rate or price rate
X = number of goods or services
C = flat rate or gate fees
The business can also operate differently by using exponential equation
A = P(1 + R%)^t
Where
A = profit
P = capital
R = rate
t = time
PLS HELP! I need help with Non-Linear Data on a graph with scatterplot.
Answers
The function increased to a maximum value and then decreased.
How do you identify trends in a data plot?We know that a graph can be obtained when we plot the points of the data on a graph. In this case we can see that the data have been graphed accurately as we can see here.
If we look at the graph, we can see that the graph went up and then it started coming down. The implication of that is that the function has attained a maximum point and then began to decrease.
This is clear from the graph that has been shown.
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explain why 8 < x < 2 has no solution? need the answer quick
Answers
Answer:
8 < x < 2 has no solution because there is no number greater than 8 (8 < x), yet less than 2 (x < 2). It's impossible, so there is no solution.
If the inequality was something like 8 < x < 10, then it will work because 8 can be less than x and x can be less than 10.
Hope this helps and have a great rest of your day! :)
a cylinder has20,7.5cm surface and another cylinder has 20,20,7.5cm (a)Which shape has the greater surface area? (b)By how much is it greater?. (c)Which shape has the greater volume? d) By how much is it greater?
Answers
(a) Cylinder 2 has the greater surface area.
(b) Cylinder 2 has a surface area 471.2389 cm² greater than Cylinder 1.
(c) Both cylinders have the same volume.
(d) There is no difference in volume between the two cylinders.
Define surface area and volume of cylinder?The sum of the curved and flat surfaces that make up a cylinder is its surface area.
The formula for calculating a right circular cylinder's surface area is,
A = 2πr² + 2πrh, where h is the height of the cylinder and r is the radius of the circular base.
The volume of a cylinder is how much space it covers. The volume of a right-angle cylinder can be calculated using the formula,
V = πr²h, where h is the height and r is the radius of the circular base.
Here question given that,
For Cylinder 1:
Surface area = 20,7.5 cm = 471.2389 cm² (rounded to 4 decimal places)
Volume = πr²h = π(7.5/2)²(20) = 1767.1459 cm³ (rounded to 4 decimal places)
For Cylinder 2:
Surface area = 20.20.7.5 cm = 942.4778 cm² (rounded to 4 decimal places)
Volume = πr²h = π(7.5/2)²(20) = 1767.1459 cm³ (rounded to 4 decimal places)
(a) Cylinder 2 has the greater surface area.
(b) Cylinder 2 has a surface area that is 942.4778 - 471.2389 = 471.2389 cm² greater than Cylinder 1.
(c) Both cylinders have the same volume.
(d) There is no difference in volume between the two cylinders.
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PLEASE HELP I WILL MARK BRAINLIEST
Answers
Answer:
I think its d
Step-by-step explanation:
helppp!!!! please!!!
Answers
Answer:
35Option A is the correct option.
Step-by-step explanation:
Angle subtended by an arc at the centre is double of the angle subtended by the same arc anywhere in the major segment.
Angle BAC:
\( \frac{1}{2} \times angle \: boc \\ \\ = \frac{1}{2} \times 70 \\ = 35\)
Good luck on your assignment..
Area in picture below
Answers
Answer: 1716/25 or 16 68/25
Step-by-step explanation:
Formula: 1/2 x height x (a+b)
HELP PLEASE
What is 2/455 as a percent?
Enter your answer as a decimal rounded to the nearest hundredth of a percent.
Answers
Answer:
0.44%
Step-by-step explanation:
1. We know that 2/455 is the same as 2÷455.
2. Once, you do 2÷455 it gives you 0.0044.
3. Then multiply by 100, 0.0044×100= 0.44%
Or just bring the decimal back two places to find this.
What is the constant term in the following expression?
4x - 2y + 3
Answers
The constant term in the expression is 3.
The expression is 4x ₋ 2y ₊ 3.
Here in this equation we have variables and constants.
variables = x and y whose coefficients are 4 and ₋2 respectively.
A variable is anything whose value can change and is not fixed. Typically, the letters x, y, z, etc. are used to indicate variables.
The above equation is in the form ax ₊ by ₊ c
An object with a fixed value in a circumstance is said to be a constant. We are aware that the constant is fixed, even though we do not know its exact value. In general, constants are represented by the letters a, b, c, p, q, etc. if their values are unknown or not given, and by particular numerical values) if their values are known.
Hence we get the constant term as 3.
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Solve the system and determine whether it is consistent or inconsistent and dependent or independent.
2x – 4y = 10
-12x + 24y = -60
Answers
It is consistent and independent.
x=25, y=10
what is the linear equation for slope= 5 (4,7)
Answers
Answer:
23.5
Step-by-step explanation:
what is the circumfrence of a dinner plate if the diameter is 10.5
Answers
Answer:
\(\huge\boxed{\sf C = 32.99 }\)
Step-by-step explanation:
Given that,
Diameter = 10.5
We know that,
Circumference of a circle = πdSo,
C = π(10.5)
C = 32.99\(\rule[225]{225}{2}\)
Function g is a transforamtion of the parent cosine function such that g (x) =3cos(x+2)+1 which paragrsugh representz g?
Answers
The correct option is (C) The graph of Function g is a transformation of the parent cosine function such that g(x) = 3 cos(x + 2) + 1 as it the graph of cosine function.
The ratio between the adjacent side and the hypotenuse is known as the cosine function (or cos function) in triangles. One of the three primary trigonometric functions, cosine is the complement of sine (co+sine) and one of the three main trigonometric functions.
A graph is a structure that resembles a set of objects in mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "related." The objects are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
Option (C) gives a graph of the parent cosine function is transformed into function g such that g(x) = 3 cos(x + 2) + 1 on the cosine function graph.
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Answer:
see photo
be sure to look closely, the top curves go to 4 and the bottom goes to -2, there are 2 with this same shape but the other one does not go high enough.
Step-by-step explanation:
Plato/Edmentum
The perimeter of a regular pentagon is 100 centimeters. how long is each side?
a. 100 cm
b. 40 cm
c. 20 cm
d. 80 cm
Answers
The correct option c. 20 cm, is the length of each sides of the regular pentagon.
Explain the term regular pentagon?Every side of a regular pentagon has the same length, and its five angles are all the same size. A pentagon is said to as irregular if its side length as well as angle measurement are not equal.A quadrilateral with five equal sides is known as a regular Pentagon.
Regular pentagon perimeter equals 5*side
Since we already know that a normal pentagon's perimeter is 100 cm.
Hence, 100 = 5*side
Side = 20 cm
Each side is 20 cm long.
As a result, the side of a regular pentagon is 20 cm long.
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