Question: Given thatX and Y are two independent random variables from an exponential distribution with parameter 6. Let U =3X2and V=X+Y. a) Determine f(x,y),thejoint probability density

Given thatX and Y are two independent random variables from an exponential distribution with parameter 6. Let U =3X2and V=X+Y. a) Determine f(x,y),thejoint probability density function of Xand Y . b) By using the transformation technique, determine the joint density function of U and V

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Problem 3: Let WI, ..., Wz be a random sample from an Exponential distribution with density f(w|B) = Bexp (-wB) for w > 0, with B >0, and let Z be a zero-truncated Poisson random variable with p.d.f....

MATH S350 TMA 01 Hints Question 1 Let A and B be the event that water is contaminated with excessive amount of pollutant A and pollutatnt B respectively. Remarks: 1. Half of those communities whose...

James and Daniels. They decided to study separately for their exam. The probability that Jack will make an "A" in statistics is 0.6, and the probability that Sam will make an"A" is 0.3. Find the...

9. Let X and Y have joint density function f (x, y) = ( 1 4 (x + 3y)e(x+y) if x, y 0, 0 otherwise. Find the marginal density function of Y. Show that P(Y > X) = 5 8 . 10. Let Sn be the sum of n...

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

7 Let U1 and U2 be two independent random variables, both uniformly distributed over [0, a]. Let V = min{U1, U2} and Z = max{U1, U2}. Show that the joint distribution function of V and Z is given by...

can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...

Answer all the questions accordingly Problem 1 Suppose a sequence of random variables is generated as follows. Let X] ~ uniform(0, 1), and X2 X] ~ uniform(X1, 1). In general, let Xxtil(X1, ..., Xx) ~...

solve these problems Consider a small ferry that can accommodate cars and buses. The toll for cars is $3, and the toll for buses is $10. Let X and Y denote the number of cars and buses, respectively,...

#1 STA355H1F due Wednesay, October 5, 2016 Problems to hand in: 1. Suppose that X1 , , Xn are independent Exponential random variables with density f (x; ) = exp(x) for x 0 where > 0 is an unknown...

1. Provide a detailed description of the service encounter. (Figure 10.1 in the Service Marketing textbook is a great resource for this assignment!) a. What are your initial perceptions? Be mindful...

The following hands-on test is designed to be presented to students after completing all chapters of the textbook. All modules are used. Students are expected to enter data for one month and then...

If you are selling a property you want the Cap rate to be ?

If Xn is a bounded increasing sequence, then Lim (X,) = n- 00 1) co 2) zero 3) Inf (Xn) 4) Sup ( Xn) Select one: 2. 3 4.

One of the following is true: 1) If f and g are increasing, then f.g is increasing. 2) If f and g are uniformly continuous then f.g is uniformly continuous. 3) If f is uniformly continuous on [0,1],...

Lim (n !)" n 00 1) e 2) e-1 3) one 4) zero

If f(x) = x, on 0, , then the value ofk that satisfies Lipschitz condition is 1) k = 1 2) k= 3) k = 2 4) k= 4

Guess the unknown organic compound with the help of the following data and explain it. IR Spectrum of the Unknown Organic Compound 4000 3000 2000 1500 1000 500 MS Spectrum (El) of the Unknown Organic...

I need help my due in less than 40 min please help !!! Max 300 - 400 words Short Case Study Marks-6.5 As part of this initiative, McDonald's selected Dynamix dairy from Baramati, Maharashtra as their...

The background knowledge of the interpreter

The expert rule: We have more confidence in information presented by someone who is an expert in the field than by someone who is not.

How easy the information is to remember