2. The proportion of the budget for a certain type of industrial company that is allotted to environmentaland pollution control is coming under scrutiny. A data collection project determines that thedistribution of these proportions is given byf(y) = {2(1- y)*,0< ys 1,elsewhere.a. Find the value of k that will make f (y) a valid density function for the above problem.b. Derive the cumulative distribution function F(y)c. What is the probability that a company chosen at random expends less than 10% of its budget onenvironmental and pollution controls?d. Determine the variance of the function f(y).

The proportion of the budget for a certain type of industrial company that is allotted to environmental and pollution control is coming under scrutiny. A data collection project determines that the distribution of these proportions is given by f(y) = (1 – y)*, 0

The proportion of the budget for a certain type of industrial company that is allotted to environmental and pollution control is coming under scrutiny. A data collection project determines that the distribution of these proportions is given by f(y) = (1 – y)*, 0

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: d For any y2, 0 < ysI what is the conditional density function of Y, given that Y2 = y;? e Find P(.3…

A: d. From the given information, fy1,y2=1, 0≤y1≤1, 0≤y2≤1 Consider, the marginal density function of…

Q: In 1950 an experiment was done observing the time gaps between successive cars on the Arroyo Seco…

A: Observe the given facts as follows.

Q: Assume the proportion of the time within a year, Y, and any flood by Kucuk Menderes River is…

A: Given: Y is the proportion of time within a year. fy=51-y4 0<y<10…

Q: Suppose X and Y have a joint density function given by C. x²y, for 0 < y < x < 1, 0, f (x, y) =…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…

Q: 13 Find the total mass of a 1 meter rod whose linear density function is p(x) kg/m for (x + 2)?

A: Linear density is defined as the mass per per unit length.Formula is given by,p(x) = massunit…

Q: Obtain the generating functions using the composition method of the following density functions f(x)…

A: The moment generating function is, MX(t)=E(etx) The characteristic function is, φX(t)=E(eitx) The…

Q: Suppose Gabriel's Horn is built out of a material with nonuniform density, and assume the function…

A: The volume of a solid can be given as the product of the cross-sectional area and the thickness. The…

Q: 4. If the joint density function of X and Y is glven f(x, y) = (x+ 2y),0 <x< 1;1<y< 2 0, elsewhere…

Q: Example 15: (i) Find the M.L.E. of the parameter a of the population having the density function…

Q: The time X (min) for a lab assistant to prepare the equipment for a certain experiment is believed…

Q: Consider the joint PDF fx.x(x,y) given in the following. f x. y(x;y)= {* ( + y?) if 0 <x<1, 0<y<1…

A: Solution: Note: Hello! As you have posted more than 3 sub parts, we are answering the first 3…

Q: 6. If the density function of X is known, the density function of Y = g(X) can be found from the CF…

Q: 9. Find the mass of a car antenna that is 3 ft long (starting at x = 0 and has a density function of…

A: 9. Given that a car antenna that is 3 ft long (starting at x=0) and has density function p(x)=3x+2…

Q: Find the mass of the following thin bars with the given density function. r1x2= 5 e-2x, for 0 … x ……

A: Given: Density function r(x)=5 e-2x where 0≤x≤4 To determine: Mass of an object.

Q: If X is uniformly distributed over (0,1), find the density function of Y = eX

A: Solution

Q: Show that the gamma density function with parameters a> 1 and A >0 has a relative maximum at…

A: We have given that To determine relative maximum we differentiate the given pdf and equat to zero.

Q: Let Y1,...,Yn denote a random sample from the density function given by fr (vla, 0) 1 ya-le- for y>…

A: Given, Y1,Y2,..Yn be the random sample and the gamma distribution function is,…

Q: The weekly demand X for kerosene at a certain supply station has a density function given by [x for…

A: a) P12≤X≤32=P12≤X≤1+P1≤X≤32=∫121xdx+∫13212dx=x22121+12x132=122-1222+1232-12(1)=58

Q: (a) Find the marginal density function for Y,. f2(Y2) = , where (b) For what values of y, is the…

Q: Is the function defined as follows a density function? fx (x) = 0 for x 4

Q: Find (a) Marginal density f X2 (b) Conditional density of the first, given that the second takes on…

Q: Given the joint density function: (6 – x – y f(x,y) = if 0 < x < 2 and 2 < y < 4; 8 otherwise. The…

A: Given that f(x, y)=6-x-y8 for 0<x<2 and 2<y<4.So the marginal distribution h(y)…

Q: (a) By finding the marginal density fy(y), show that Y ~ Exp(1).

Q: Find the mass of the thin bar with the given density function. P(x) =x/14-x; for 0sxs3

Q: If and Y have the joint density function 2e-(*+y), 0<x<y<∞, f(x,y)= 0, Otherwise. Then the marginal…

A: From the provided information,

Q: The two-parameter gamma distribution can be generalized by introducing a third parameter y, called a…

A: Mean = alpha*beta+Gamma =12*8 +44 =140 Standard deviation = beta*sqrt(alpha) = 8*sqrt(12) =27.71…

Q: If the joint density function of X and Y Is given Sk(x+2y), 0 <x< 1;1<y<2 0, elsewhere f(x,y) = a.…

A: From the given information, fx,y=kx+2y, 0<x<1, 1<y<2 The value of k is obtained below:…

Q: If the joint density function of X and Y is given S(x, y) = {k(x + 2y), 0 < x < 1; 1 < y< 2 0,…

Q: Find the mass of the following thin bars with the given density function. r1x2= 1 + x3, for 0 … x ……

A: It is given that, r(x)= 1 + x3, for 0 … x … 1 We have to find the mass of the following thin bars…

Q: as the density function p(x 0.5X

Q: For x1, the marginal distribution fx1 (x1) function is valid is it a density function)

Q: 9. Find the mass of a car antenna that is 3 ft long (starting at x = 0) and has a density function…

A: Given that a car antenna is 3 ft long (starting at x=0) and has a density function of ρ(x)=3x+2…

Q: 3. (a) Find the mass of a thin wire shaped in the form of the semicircle y = v9 – x²2 if the density…

A: The given problem is to find the mass of thin wire placed in the shape of semi circle with given…

Q: 1 Solve the below problem: et Y1 and Y2 have a joint density function given by

A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

Q: elsewhere If Y = X be a function of X, find the density function of Y using method of distribution…

Q: A privately owned liquor store operates both a drive-in facility and a walk-in facility. On a…

A: a) The marginal density function of X is given below:…

Q: 4. Find the mass of a thin bar having the linear density function p(x)=6+x', defined over the range…

Q: 4. Let X and Y denote the lengths of life, in years of two components in an electronic system. If…

A: Given: fx, y=e-x+y, x>0, y>00, otherewise

Q: Find the mgf of Y = 1 – e-AX when X ~ Exp(A). Note that the density of X is given in the last…

A: X ~Exp(λ) So, PDF of X is given by, f(x) = λe-λx , x>0 Therefore The CDF of X is given by, F(x)…

Q: 5. If the characteristic function of a continuous RV X with density function = S ø(@) e-ix@ dø. 2…

Q: then what is the marginal density function of X, where nonzero?

Q: 5) For the following density function f(x) =c x2 (1 –x), 0<x<l, 1) Find the constant c 11) Find Mean

Q: 4.14 Find the proportion X of individuals who can be expected to respond to a certain mail-order…

A: Given,f(x)=2(x+2)5 ; 0<x<10 ; elsewhere

Q: below. (6 – x – y) 0<x<2,2<y<4 f(x,y)= otherwise a) P(X< 1,Y < 3)=? b) P(X< 1/Y < 3)=? c) Find the…

A: Dear Student, We are allowed to solve only the first three parts , Please ask the last part…

Q: Let X have the uniform distribution on the interval [1, 3]. Find the density function of Y =X^2.

Q: 5.Suppose X is a continuous variable with density function -l<x<1 f(x) ={2" 0,0therwise a)Compute…

A: From the given information, Consider, X be the continuous random variable with density function as…

Q: 1. Compute E[X] and Var(X) if X has a density function given by Gxe-x/2 x > 0 (0, otherwise a. f(x)…

Q: 1 'If fx(x)=- -x² /2 find the density function for Y

Q: Find the mass of the thin bar with the given density function. 2 p(x)=x√ 16-x; for 0≤x≤3

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

100%

2. The proportion of the budget for a certain type of industrial company that is allotted to environmental
and pollution control is coming under scrutiny. A data collection project determines that the
distribution of these proportions is given by
f(y) = {2
(1- y)*,
0< ys 1,
elsewhere.
a. Find the value of k that will make f (y) a valid density function for the above problem.
b. Derive the cumulative distribution function F(y)
c. What is the probability that a company chosen at random expends less than 10% of its budget on
environmental and pollution controls?
d. Determine the variance of the function f(y).

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

For a certain psychiatric clinic suppose that the random variable X represents the total time (in minutes) that a typical patient spends in this clinic during a typical visit (where this total time is the sum of the waiting time and the treatment time), and that the random variable Y represents the waiting time (in minutes) that a typical patient spends in the waiting room before starting treatment with a psychiatrist. Further, suppose that X and Y can be assumed to follow the bivariate density function fXY(x,y)=λ2e−λx, 0<y<x, where λ > 0 is a known parameter value. (a) Find the marginal density fX(x) for the total amount of time spent at the clinic. (b) Find the conditional density for waiting time, given the total time. (c) Find P (Y > 20 | X = x), the probability a patient waits more than 20 minutes if their total clinic visit is x minutes. (Hint: you will need to consider two cases, if x < 20 and if x ≥ 20.)
Suppose f(x)=3x2, 0<x<1 is a density function of X. Find P(1/2<X<2).
Suppose that X and Y have a joint probability density function f(x,y)= 1, if0<y<1,y<x<2y; 0, otherwise. (a) Compute P(X + Y less than or equal 1). (b) Find the marginal probability density functions for X and Y , respectively. (c) Are X and Y independent?
The PDF of a continuous random variable X is as follows: f(X)= c(4x2 - 2x2) 0<* x <* 2 (*less or equal to) a. For this to be a proper density function, what must be the value of c ?
With the known values of a = 200,000 and b = 230,000, the first equation for the probability density function for the sales price of a home is found as follows. f(x) = 1/b – a, a ≤ x ≤ b = 1/230,000 − 200000, 200,000 ≤ x ≤ 230,000 = 1/30000, 200,000 ≤ x ≤ 230,000 Everywhere else, the probability density function will just be 0. Therefore, the full probability density function for the sales price of a home follows. f(x) = _______________ 200,000 ≤ x ≤ 230,000 elsewhere
Suppose that the joint probability density function of X and Y is fX,Y(x,y) = 10.125(x2 – y2) e−3x , for 0<x<∞ and -x<y<x 0, otherwise Give your answers to the below questions in two decimal places where appropriate. (a) The marginal probability density function of X is given by: fX(x) = A xB e-3x , for 0<x<∞ 0, otherwise Find the value of A. (b) Find the value of B. (c) The conditional probability density function of Y, given that X=x for some x>0, takes the following form: fY|X=x(y) = C (x2-y2) xD e-Ex, for -x<y<x 0, otherwise. Find the value of C (d)Find the value of D. (e)Find the value of E.
Suppose X and Y have a joint density function of f(x,y)=6x2y, 0<x<1, 0<y<1. Find P(X+2Y<1).
Suppose that Y1, . . . , Yn is a random sample from a population whose density function is
5. Suppose that the joint probability density function of X and Y is given by f(x, y) = C (x² + y), 0 < x < 2, 0 < y < 2 and f(x, y) = 0 otherwise. (a) Find C. (b) Find the marginal density functions of X and Y. (c) Compute P(X > Y). (d) Compute E[X]. (e) Compute E[Y].
5.)Suppose X is continuously uniformly distributed on [1, 4]. Let Y = ln(X). What is the density function for Y ? (Include the bounds for Y .)
Suppose that X has the density function c(x) = CX2 for 0 ≤ x ≤ 1 and f(x) = 0 otherwise.a. Find c.b. Find the cdf.c. What is P(.1≤ X <.5)?
Suppose you choose a real number X from the interval [2, 10] with a density function f(x) = 1/48x. Find P(X > 5)