1. Consider the joint pmff(x, y) for the discrete random variables X and Y:2xy²30f(x, y) =x = 1, 2, 3;y = 1, 2Determine the marginal distributions of X and Y, and then determine if X and Y independentusing these distributions.

Answered: f(x, y) = 2 xy² 30 x = 1, 2, 3; y = 1,…

f(x, y) = 2 xy² 30 x = 1, 2, 3; y = 1, 2 Determine the marginal distributions of X and Y, and then determine if X and Y independent using these distributions.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: Find marginal distributions P(x) and P(y)

A: The objective is to construct the marginal distribution of P(x) &P(y) Given that the joint…

Q: Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial…

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

Q: Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial…

Q: The present value of y dollars after x years at 15% continuous interest is f (x, y) = ye-0.15x.…

A: Given, f(x,y)=ye-0.15x

Q: For the joint distribution function f(x,y)=2 for x≥0,y≥0,x+y≤1 and 0 otherwise Find the marginal…

A: The joint probability function is f(x, y)=2 for x≥0,y≥0,x+y≤1 0 otherwise

Q: Calculate the standard deviation of x and y, then the correlation(x,y)

Q: Var(Z)=(10)E(Z) Find the distribution of Z and find its parameter(s)

Q: 6. A chemical system that results from a chemical reaction has two important components among others…

A: Given, the joint distribution of X1 and X2 is

Q: viation and high-altitude physiology is a specialty in the study of medicine. Let x = partial…

A: n = 5 , For(b) it is one tailed test

Q: Y₁ (a) Find the joint pdf of (V,, V₁, V₂), where V₁ V₂ and v₁ - (b) Find the marginal pdf of V₂.

Q: k рех, у) хсу. y = 1,2,3 other - and the marginal probability function of Y P (Y) 6

A: Given PDF is p(x, y) = kx2y,x=1, 2, y=1, 2, 30,otherwise

Q: Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial…

A: The data for two variables x and y are given.

Q: The normal distribution is a bell-shaped curve defined by f(x) = e-x*,x € [-4,4] Optimize the…

Q: E[X] and E[Y] and variances VAR[X] and VAR[Y]. (to be used below in CORR(X,Y)) Using part b, Can you…

Q: Aviation and high-altitude physiology is a specialty in the study of medicine. Let x - partial…

A: Solution: Given data is x 6.7 4.9 4.2 3.3 2.1 (units: mm Hg/10) y 42.0 34.5 26.2 16.2 13.9…

Q: If Y₁ = ettet-1+e-2 3 ', PY₁,Y₁-2 find E(Y), var(Y), cov (Yt, Yt-1), cov (Yt, Yt-2), PY,Y, and…

A: Given that,and is an iid (independent and identically distributed) random variable with zero mean…

Q: Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial…

A: Given the variables, the partial pressure of oxygen in the alveoli (air cells in the lungs) when…

Q: The joint pmf of a bivariate RV (X, Y) is given by p(x, y) = = Ska²y, x= 1,2; y = 1,2,3 otherwise…

A: Given that We have to find a..Value of k b..the marginal density of x and y c..check whether X…

Q: Given a normal distribution with u = 35 and o = 6, find (a) the normal curve area to the right of x…

A: As per guideline expert have to answer first three subparts only.

Q: Researchers decide to run a resume-based audit study where they randomize names based on gender…

A: Given that Researchers decide to run a resume-based audit study where they randomize names based on…

Q: • If the joint PDF of X and Y is shown as follows: fxx(x, y) = e-(x+y) Find the following: 12) The…

Q: Then the variance of Y is

A: Given, E(Y/X=x)=2xvar(Y/X=x)=4x2 f(x)=1, 0<x<10, e.w

Q: 2. Two independent variables X and Y have a distribution function F(x)=x and F(y)=y respectively, if…

Q: Aviation and high-altitude physiology is a specialty in the study of medicine. Let x- partial…

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

Q: Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial…

Q: Find the mar gin al distribution of X. Find the margin al distribution of Y. Are X and Y…

A: For the independence of two variable X and Y, we must have f(x, y) = f(x).f(y)

Q: Consider the joint PDF f(x,y)=4xy for 0<x<1 and 0<y<1. (a) Are X and Y independent? (b) Find both…

A: We have given thatjoint PDF f(x,y)=4xy for 0<x<1 and 0<y<1.

Q: a JPDF f(x,y) = 8/81 xy for 0<x<3 and 0<y<x. Let V(X) = 5.76 and V(Y) = 2.56 Find the correlation…

A: Solution:f(x,y) = 818 where, 0 < y < x & 0 < x < 3 So,E[xy] =…

Q: (16) Let X U(3) find Var-x) and distribution function.

A: Given: Let X be a random variable that follows discrete uniform distribution. Mathematically, X~U(n)…

Q: 3E1. An interval estimate is a range of values us to estimate (a) the shape of the population…

A: Here, need to find out the correct choice for the given statements Note: According to Bartleby…

Q: Let D region be limited by x=0, y=1 and y=x lines. What is the mean value of f(x,y)=xy function in D…

Q: The following holds marginal pdf of X P(X > 3) = re-#(1+y) dy dx = xe-". e¬#" dy dx e¬ª dx = 0.05.

A: Here the objective is to prove that PX>3=0.05.…

Q: kxy Let f(x,y) = " be the joint probability mass function with x, y = 1,2,3. %3D 6. iv. Construct…

Q: 7. (25 points) Let X have the pdf f(x) = 2, -2 < r < 4. Find the pdf of Y = X² using Two-to-one…

Q: Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial…

A: Since you have posted a question with multiple subparts, we will solve first three subparts for you.…

Q: Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial…

A: b) From the provided information, Coefficient of correlation (r) = 0.985 Hypotheses are:

Q: Describe the types of probability samples and discuss under which conditions they may be the most…

A: Solution-: Describe the types of probability samples and discuss under which conditions they may be…

Q: The joint distribution of X and Y is: Pxy(0,0)=1/15, P (0,1)=a, Py(0,2)=2/15 X,Y X,Y X,Y Pxy(1,0)=a,…

A: Solution

Q: Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy…

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

Q: 6. Let X1) be the minimum value in a sample of n independent observations from the distribution with…

A: Pdf of first order Statistic is f(x) =n[1-F(x)]^(n-1) f(x)

Question

1. Consider the joint pmff(x, y) for the discrete random variables X and Y:
2
xy²
30
f(x, y) =
x = 1, 2, 3;
y = 1, 2
Determine the marginal distributions of X and Y, and then determine if X and Y independent
using these distributions.

Expert Solution

Step 1

It is given that the joint pmf f(x,y) for the discrete random variables X and Y is

f(x,y) = xy²/30, x = 1, 2, 3; y = 1, 2

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

A) | kx 0 1 B) Obtain the 25th percentile and the 75th percentile of the distribution.
Find the slope of the normal line to the graph of f(x) = (2x + 1)² at the %3D point where x = 3. O 14 1 28 1 14 O 28
3 500 0≤x≤ys 10 1. Find the marginal distribution of Y with appropriate support. f(x, y) =
R3
Ex 2 Let y (0) = X~ Bin (₁0) 3 € = 01102 {0.4 Posterior distribution Find e € [0, 1]
X f (x, y) 2 4 1 0.10 0.15 T 3 0.20 0.30 5 0.10 0.15 a. Determine the marginal distribution g(x), x = 2, 4. b. Determine the marginal distribution h(y), y = 1, 3, 5.
Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial pressure of oxygen in the alveoli (air cells in the lungs) when breathing naturally available air. Let y = partial pressure when breathing pure oxygen. The (x, y) data pairs correspond to elevations from 10,000 feet to 30,000 feet in 5000 foot intervals for a random sample of volunteers. Although the medical data were collected using airplanes, they apply equally well to Mt. Everest climbers (summit 29,028 feet). (units: mm Hg/10) (units: mm Hg/10) 6.5 5.4 4.2 3.3 2.1 y 43.6 32.3 26.2 16.2 13.9 Ex = 21.5, Ey = 132.2, Ex² = 104.35, Ey2 = 4086.34, Exy = 650.51, and r= 0.978. %3D Ex 21.5 Ey 132.2 Ex2 104.35 Ey2|4086.34 Exy 650.51 r 0.978 Use a 1% level of significance to test the claim that p > 0. (Use 2 decimal places.) critical t Verify that S. - 2.9006, a = -3.208, and b = 6.895. e Se a b Find the predicted pressure when breathing pure oxygen if the pressure from breathing available air is x…
Let Y, and Y, have a bivariate normal distribution. The marginal distribution of Y, is normal with mean u, and variance o, f(y1) = 20í ,-0 < yı < ∞, V2no, Calculate the marginal distribution of f (y2).
9
Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial pressure of oxygen in the alveoli (air cells in the lungs) when breathing naturally available air. Let y = partial pressure when breathing pure oxygen. The (x, y) data pairs correspond to elevations from 10,000 feet to 30,000 feet in 5000 foot intervals for a random sample of volunteers. Although the medical data were collected using airplanes, they apply equally well to Mt. %3D Everest climbers (summit 29,028 feet). (units: mm Hg/10) (units: mm Hg/10) 7.3 4.6 4.2 3.3 2.1 42.4 31.7 26.2 16.2 13.9 (a) Verify that Ex = 21.5, Ey = 130.4, Ex = 107.39, Ey = 3944.74, Exy = 648.03, andr 0.969. Σχ 21.5 %3D %3D Ey 130.4 Ex2 | 107.39 Ey2 3944.74 Exy 648.03 r0.9686 (b) Use a 10% level of significance to test the claim that p > 0. (Use 2 decimal places.) t 6.79 critical t 1.6377 Conclusion Reject the null hypothesis, there is sufficient evidence that p > 0. Reject the null hypothesis, there is…
(b) Determine the marginal distributions of X and then of Y. (c) Find the conditional distribution of Y|X = x.
6. Suppose you walk a hiking trail at a speed which is uniformly distributed from 4 to 6 miles per hour. The distance of the trail is 24 miles. Find the PDF of the duration of the trip. (Note: speed = distance/time)