(a) What value of c makes this a joint pdf?(b) Find the marginal distributions for X and Y .(c) Are X and Y independent? Explain how you know. Let X and Y be continuous random variables with joint probability density functionf (x, y) = {cxy 0

We want to find (i) the value of c (ii) Marginal of X amd Y (iii) Check whether it is independent…

Answered: (a) What value of c makes this a joint…

(a) What value of c makes this a joint pdf? (b) Find the marginal distributions for X and Y . (c) Are X and Y independent? Explain how you know.

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: 2. For the Cauchy distribution: 1 C(x; γ) %3D 2 (X – Xo - TY |1 + a. Derive the mean of the…

A: Given the Cauchy distribution , C(x;γ)=1πγ[1+(x-x0γ)2 ] To derive mean of the distribution and the…

Q: (b) Find marginal distributions of X and Y. (c) Find Conditional distributions of X given Y and Y…

Q: wo components of a minicomputer have the following joint pdf for their useful lifetimes X and…

Q: 2. Let X and Y have joint pdf 1 f(x, y) = x² + 0 < x < 1,0 < y < 2 (a) Find the marginal…

Q: A random variable X has a pdf 1 cosx ーπ fx (x) ={2 2 2 elsewhere Find the mean value of the function…

Q: Find the expectation of XY. Find the covariance Cov(X, Y) between X and Y. What is the correlation…

A: According to our guidelines we are solving only first three sub-parts of given question and the rest…

Q: a. Find the marginal density of X. b. Find the marginal density of Y. c. Find the probability that…

Q: (a) Find EY and Var Y. (b) Find the joint distribution of X and Y. (c) Find the marginal…

Q: Q1: Let X1, ... Xn be a random sample from exponential distribution with a mean of 8. Show that Y1 =…

A: Given: Let X1, X2, ..., Xn be a random sample from exponential distribution with a mean of θ.

Q: Let the random variable X follow a gamma distribution with α = 4 and β = 4. If Y = X2 what is the…

A: Given, X~ Gammaα=4,β=4 Y=X2

Q: The Lorenz curves for the income distribution in the United States for all races for 2015 and for…

Q: lom variable X is given below. fx(x) 1 2 a random variable Y, where whose PDF is given below. fy(y)

A: *Answer:

Q: The joint pdf of two continuous random variables is given by f(x,y) = 6x²y, 0 0.5) (b) Find the…

A: According to bartleby policy I have solved first three subparts of this question....

Q: Suppose the random variable Y has an exponential distribution with mean 2. Use the method of…

A: The random variable Y has an exponential distribution with mean 2.

Q: Calculate SSb and SSw Calculate dfb and dfw Calculate MSb and MSw Calculate F Identify the…

A: Null hypothesis H0: There is no significant difference between academic standing of students who sit…

Q: Let Y - X². (a) Find the pdf of Y when the distribution of X is normal N(0, 1). (b) Find the pdf of…

A: Part (a) Express the mathematical relation to calculate the probability density function in normal…

Q: Let the density function of random variable x be given by fx(x) =0x^0-1, 0<x<1 Suppose x1, x2.. Xn…

A: Given,

Q: Find the mean and variance for the distribution of random variable X whose density function is f(x).…

Q: c) A continuous random variable X takes values in the interval 1 < x< 3and the probability density…

A: Probability density function is used to give the probability distribution of a continuous random…

Q: Let X represent the lifetime in months of a certain brand of light bulb. The pdf of X is given by…

Q: 1 0.8 2 0.6 0.4 0.2 0 1 3 4 y A.Is Y discrete or continuous? Explain. Plot the PMF/PDF of random…

A: Solution

Q: 6. Show that a gamma distribution with a> 1 has a relative maximum at x = (a- 1)B. What happens when…

A: We have to show that : gamma distribution with alpha >1 has a relative maximum at x=(alpha -…

Q: b) Find the marginal probability density function of Y, fy (y).

Q: (1) The value of 'C' (ii) Marginal distribution functions of X and Y.

Q: 1. Find the mean and variance for the distribution of random variable X whose density function is…

A: f(x)=116 x2 e-x2 x>0 =0 otherwise mean for the distribution of…

Q: the conditional pdf of Y given X.

A: The joint pdf is f(x,y)=k(x+y) 0≤x≤y≤10 otherwise then value of k…

Q: marginal distribution g(x).

A: Let the given Joint Probability density function is f(x,y)=x+y3…

Q: Scores on a freshman chemistry test are described by the pdf f(y)=6y(1-y) for 0sys1 where Y…

A: Scores on a freshman chemistry test are described by the pdf given by : f(y) = 6 y ( 1 - y ) for…

Q: (iii) Find the marginal pdf's (iv) Find the joint cdf

Q: 0, x< 0, F4(x) = (, x20. 1- 0.3e-0.00001x For the above model, determine the following: a. Mean…

A: Given F4x= 0 , x<01-0.3e-0.00001x , x≥0

Q: (a) Give the marginal density of X1. (b) Give the marginal density of X2. (c) Give the conditional…

Q: The(probability density function of a random variable, x is (x) = -(4 – x²) for 0< x < 2 4 = 0 %3D…

A: Introduction :

Q: Example 2.17 Let X be a continuous type random variable with PDF given as f(x) = 27 Let Y be another…

Q: Let X and Y be two random variables with the joint pdf as shown in the picture. a. Calculate P (X…

A: "Since you have posted a question with multiple subparts, we will solve first 3 sub-parts for you.…

Q: 7. Suppose that X- Normal (u,o²). (a) Find the PDF fy(y) of Y = e, and then sketch the graph of fy…

A: 7) Given that X follows normal with mean μ and variance σ2 The probability density function for X…

Q: ke-3x Let f(x)= 0 < X < 0 %3D be pdf of the random variable X. otherwise

A: Given,f(x)=ke-3x ;0≤X≤∞0 ;otherwise

Q: 2. Find the equation of the normal line of the curve y 2 - xe y-1 + x 3 = 7 at (2,1).

A: As per your request, we will solve Q-2.

Q: The lifetime of a machine part has a continuous distribution on the interval (0,45) months with…

A: Given that f(x) is proportional to (4+x)-2. So, f(x)=k(4+x)-2 , 0<x<45 Total probability must…

Q: EXER 2.1 Let X and Y be random variables whose joint probability distribution function is given by…

Q: Let f(x) = ½ , -1 < x < 1 0 otherwise be a pdf of the…

Q: Example 1 Let X have the probability density function 2x ,0<x<k f(x) = {kz 0 ,e.w. For what value of…

Q: Two components of a computer have the follow- ing joint pdf for their useful lifetimes X and Y:…

A: Given:

Q: a) Find the moment generating function of the sum T= Y1+Y2+Y3+Y4. What is the distribution of T? b)…

Q: 1. Let X be an RV with PDF a. Find the mean of X. b. Find the variance of X. f(x) = {¹ -=| - |x| for…

Q: Find the joint probability density of = x + Y, Zz X+Y Find the marginal pdf of Z2.

A: It is an important part of statistics. It is widely used.

Q: ) Determine the value of C. ) Find the marginal PDF of X. -) Find the conditional PDF of Y given X =…

A: The conditional density of Y given X = x can be obtained as f(y | X = x) = f(x, y)/fX(x) Note :…

Q: Find the marginal density functions of X and Y.

Q: Let X and Y have the joint pdf f(x,y)= x+y , 0<=x<=1, 0<=y<=1. Calculate the mean(x)

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

Q: If Q = f (x, y) and considering increases in both variables, how is expressed the total differential…

A: Concept - By using chain rule of derivative

Question

(a) What value of c makes this a joint pdf?

(b) Find the marginal distributions for X and Y .

Let X and Y be continuous random variables with joint probability density function
f (x, y) = {
cxy 0<y< x < 1
otherwise

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

Expert Solution