. At a particular gas station, gasoline is stocked in a bulk tank each week. Let random variable X denote the proportion of the tank's capacity that is stocked in a given week, and let y denote the proportion of the tank's apacity that is sold in the same week. The joint pdf of X and Y is given by = {³x (3x 0 f(x,y) = if0≤y

. At a particular gas station, gasoline is stocked in a bulk tank each week. Let random variable X denote the proportion of the tank's capacity that is stocked in a given week, and let y denote the proportion of the tank's apacity that is sold in the same week. The joint pdf of X and Y is given by = {³x (3x 0 f(x,y) = if0≤y

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: Page 263, 4.4.5.* Let Y₁ < Y₂ < Y3 < Y4 <Y5 be the order statistics of a random sample of size n = 5…

Q: choose the correct statement for the first order stationary random process X(ts): O a the PDF…

A: A random process {X)(t),t∈J} is stationary if the statistical properties do not change by time.

Q: If the variance of a Poisson variate is 3. Find the probability that, ne (1) x= 0 (ii) 1sx<4 ca eor…

A: Given that, The variance of a Poisson variate is 3

Q: Suppose X1,..., X15 are iid with pdf f(x) = 3r²,0 < x < 1, zero elsewhere. Let X15 the sample mean.…

A: Given that fx=3x2, 0<x<1 Consider, μ=∫x=01xfxdx =∫x=01x*3x2dx =3x4401 =34 σ2=∫x=01x2fxdx-μ2…

Q: Suppose Y has a uniform pdf over the interval [3,5]. Find its (1) first quartile, its (2) median,…

Q: Let X be a discrete random variable with range Rx = {0, ), such that Px(0) = Px() = Px() = Px() =…

Q: 5. Let X have the pdf {(x + 1) -1 <x < 1 f(x) = elsewhere. Find the mean and the variance of X.

A: 5. The given pdf is, fx=12x+1 -1<x<10 elsewhere

Q: Suppose X1,...,Xn are measurements of the mass of an object. The measurements are normally…

Q: Let x = (x₁,...,xn) be a data set, and denote its sample standard deviation with sx. Let y₁ = ax; +…

Q: The weekly demand for propane gas (in 100's of gallons) from a particular facility is a random…

Q: The random variable X has PDF given by 1 f(x)=√e-2/4 -1/4 for x > 0, zero otherwise. Compute P(X> 5)…

Q: Let Y, represent the ith normal population with unknown mean , and unknown variance of for i=1,2.…

A: Given that the random variable represents the ith normal population with unknown mean and unknown…

Q: e lifetime of a machine part has a continuous distribution: Osxs40 (x) ={ (10+x)² else Calculate the…

A: Note: As per the instructions we are allowed to solve three subparts at a time. Kindly repost the…

Q: Let X be a random variable and a real number. Show that E(X - a)² = varX + (µ − a)² Hereμ = EX is…

A: E(X−a)2=E(X−μ+μ−a)2=E((X−μ)+(μ−a))2=E((X−μ)2+2(X−μ)(μ−a)+(μ−a)2)=E(X−μ)2+E(2(X−μ)(μ−a))+E(μ−a)2=E(X−…

Q: The lifetime of a machine part has a continuous distribution: Osxs 40 fx(x) = { (10+x)² else a.…

Q: Suppose that Y1,..., Yn is a sample of size n from a Exp(B), B > 0. .3B (a) Find the distribution of…

Q: Let Y, represent the th normal population with unknown mean , and unknown variance of for i=1,2.…

A: For the first variable :The sample size is .The sample mean is .The sample variance is .For the…

Q: Let X1, X2, .., X10 be a random sample from a gamma distribution with a = 3 and ß = 1/0. Suppose we…

Q: A circle of radius r has area A = r. If a random circle h

A: Given, a circle of radius r has the area A=πr2. If a random circle has a radius that is uniformly…

Q: Let X be a random variable with pdf: f(x)= k(10 - 2x) for x being [0,5] a.) Find k b.) Find E(X)…

A: GIVEN DATA : X is the random variable with probability density function fx=k10-2x in the interval of…

Q: m-1 j=) t is the distribution of Y,? State all the relevant parameters of the evel a test (that is,…

A: Write the distribution of Yi bar and state its all the relevant parametersWrite the distribution of…

Q: =. Let X, Y and Z have the joint pdf x² + y? + z x2 + y? + z2 (2т) 3/2 1+ xyz exp exp where -o < x <…

A: The joint density pdf of X, Y and Z is, fx,y,z=12π32e-x2+y2+z221+xyze-x2+y2+z22 Consider,…

Q: Assume δ = 0.05, ̄Ax = 0.06, 2 ̄Ax = 0.0040. A group of 100 lives age x purchase fully continuous…

A: Given δ=0.05 A¯x=0.06 A¯x2=0.0040 Benefit=$1000 Premium=$3.50

Q: A random sample of n volumes in the form of X1, X2, ... , Xn is taken from a population with a…

A: We have to find the log likelihood function for the normal distribution.

Q: Inspection trials are carried out in a factory to assess the quality of products. In each trial r,…

A: Given that be the number of satisfactory items in the trial and is assumed to follow the binomial…

Q: Let X1, X2,..., Xn be a random sample from a distribution with a pdf ax. ae ';x > 0 f(x) 0,…

A: X~exp(ɑ)

Q: A random variable Y has a uniform distribution over the interval (8,, e,). Derive the variance of Y.…

Q: The amount of water in a reservoir at the beginning of the day is a random variable X and the amount…

A: The amount of water left in the reservoir at the end of the day: Z= X-Y

Q: Suppose X and Y are independent. X has a mean of 1 and variance of 1, Y has a mean of 0, and…

A: According to the Bartleby guidelines expert solve only one question and maximum three subpart of the…

Q: O = Let 0, X,, X2,... be RVs. Suppose that, conditional on 0, X1, X2,... are independent and X, is…

Q: Let X = ((X,,Y),....(X, Yn)) be a sample from a bivariate normal population. how that the…

A: Given information: It is given that X be a sample from a bivariate normal population.

Q: 4. Let X₁ and X₂ be independent identically distributed random variables both having exponential…

A: Let X1 and X2 be independent and identically distributed random variables both having an exponential…

Q: Q1. Let X; and S be the mean and variance of independent random samples of size n; from populations…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: Let X Poisson(A) and Y = vX. Use the delta method to approximate the mean and variance of Y.

Q: X1,X2,...,Xn are i.i.d. random variables from N(0,θ) distribution. Here, θ= σ2 >0 is the variance of…

Question

4. At a particular gas station, gasoline is stocked in a bulk tank each week. Let random variable X denote the
proportion of the tank's capacity that is stocked in a given week, and let y denote the proportion of the tank's
capacity that is sold in the same week. The joint pdf of X and Y is given by
f(x,y) = {³x
(3x
0
if 0 ≤ y <x< 1
otherwise
Find:
a) the probability that less than half the tank is stocked and less than a third of the tank is sold in a
random week;
b) the probability that the amount of gas sold is less than half of the amount stocked in a given week.

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

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

See image for questions related to this problem.

8. (Same as #4) At a particular gas station, gasoline is stocked in a bulk tank each week. Let random variable X
denote the proportion of the tank's capacity that is stocked in a given week, and let y denote the proportion
of the tank's capacity that is sold in the same week. The joint pdf of X and Y is given by
if0 ≤y <x<1
otherwise
f(x,y) = {³x
(3x
0
a)
Find the marginal probability distributions of X and Y.
b) Show that the two random variables are not independent. Using part of your answer to a) is a much
shorter solution. Once you've done this with probability, using common sense is VERY straightforward.

Solution

by Bartleby Expert

SEE SOLUTION

Similar questions

Suppose that the lifetime in years, X, of a type of electrical switch follows the distribution f(x)=12e−x2f(x)=12e−x2for x>0x>0. What type of continuous distribution is this and what is the average lifetime of one of these switches?
We have a random variable X that is uniformly distributed on interval [-1,2]. Let Y = |X| - 1. We want to find pdf using CDF technique. What is the support and pdf for the random variable Y? What would fy(-.2) be? What about Fy(-.2) be?
Suppose X and Y are two independent variables with variance 1. Let Z = X+bY where b > 0. If Cor(Z, Y ) = 1/2, what is the value of b?
Let X1 ,X be a random sample from N(u, o?). The sample variance S2 is defined by (X- %3D n-1 im1 (n-1)S2 (a) Using the fact that two constants a and b satisfying: has a xn-1) distribution, explain how we can get (n-1)S2 S6 =1-a, (1) where a xo/2(n-1) and b xa/2(n-1) are critical values that can be obtained from a x-table. %3D
Let Y, represent the ith normal population with unknown mean #, and unknown variance of for i=1,2. Consider independent random samples, Ya, Ya, Yin, of size n,, from the ith population with sample mean Y, and sample variance S² = (₁-P) ². (d) Define V₁, a function of S1, that has a chi-square distribution. (e) Is V₁ a pivotal function to find a confidence interval for o?? Explain with argument. (f) Find a (1-a) x 100% confidence interval for of
If the random variable X as a mean of u and a variance of o2 what is the P((X-u)² < 20): O less that equal to 1/4 O greater than or equal to 3/4 cannot tell O equal to 5/4
Find the mean of random variable of X, if X is random variable with pdf f(x) = c(1-x²), -1
Show that the characteristic function of Laplace distribution ƒ(x) = 1=1/√e ²¹x²₁ е - -∞0 < x < ∞ 1 is C (0) = 1+0² Find also the mean, the variance and mean deviation about the mean. 11.
Let X1, X2,......, Xn be a random sample from an exponential population, find the moment estimator for 0.
Page 264, 4.4.12
3.4 Solve the below problem: Let Y, and Y, have a bivariate normal distribution: 2. 1. 2. Y2-H2 exp 2no,02y1-p2 2(1-p2) {. (ज-र.) + ( ज-र) (ज-पदर) 07 (जब)} Dr= –00 < y, < ∞, -00 < y2 < ∞, Show that the marginal distribution of Y, is normal with mean µz and variance o is given by: 2, 1 f(y2) = 203 ,-00 < Y2 < ∞ 2.