HW2: The joint probability density function of two discrete random variables X and Y is given by p(x, y)=c(2x+y), where x and y can assume all integers such that 0s xS 2, 0S y< 3, and p (x, y)= 0 otherwise. a) Find the value of the constant c. (c) Find P(X 21, Y <2). (b) Find P(X =2, Y= 1).

HW2: The joint probability density function of two discrete random variables X and Y is given by p(x, y)=c(2x+y), where x and y can assume all integers such that 0s xS 2, 0S y< 3, and p (x, y)= 0 otherwise. a) Find the value of the constant c. (c) Find P(X 21, Y <2). (b) Find P(X =2, Y= 1).

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: 3 nd the probability distribution of Y = (1+)² e- (²) -0.5 □e(¹-√√3/y) 3e-3x 3y y/3 f(x) = { %* 0,…

A: Let X be random variable

Q: (a) What is the probability density function of aX + bY? (b) Compute E[X|X − 2Y] and E[X²|X – 2Y].

Q: The random variables X and Y are independent to each other. The probability density functions of X,…

A: Given the pdf of the independent random variables X and Y as fXx=2x , 0<x<1 fYy=1 ,…

Q: 2. Let X and Y be continuous random variables with bivariate p.d.f. f(x, y) and let2) denőté…

A: Introduction: Here, f (x, y) denotes joint bivariate p.d.f. of X and Y, and f2 (y) denotes the…

Q: If the joint probability density function of two continuous random variables X and Y is given by…

A: Joint probability density function of two continuous random variables X and Y isgiven byf(x; y) = 2,…

Q: A and B are independent continuous random variables, determine Fc(2), where C = A+B. Note that Fe(2)…

A: # random variable x from uniform (0,4) And random variable y from exponential(1) Z=x+y Then to…

Q: 5. Let f(x,y) is a joint probability density function of (X,Y) continuous random variable as below.…

A: Dear student , We are allowed to solve first three parts, Ask the remaining part separately. f(x)…

Q: Suppose X and Y have joint probability density function 1/2 if 0 < x < 1, 0 < y < 1, 1/3 if−1 < x <…

A: Let X and Y be the continuous random variables with pdf f(x,y) given asTo find:a) The value of Cb)…

Q: (a) Let X1, X2, X3, X4 be a sample from U(0, 1), and let X(1), X(2), X(3), X(4) be the cor -…

A: The random sample from the distribution is .The corresponding order statistics are .The probability…

Q: If the joint probability density function of two continuous random variables X and Y is given by…

Q: fo 0, 947 (1-x), -0,6 $xs 0,6 (x) O.w A = %3D Find the probability density function of the random…

A: Given: The probability density function of the random variable X is given as:…

Q: X and Y are independent exponential random variables with the following joint proba- bility density…

Q: X and Y are jointly continuous with joint probability density function fxx (x, y) = { xe¯*(1+y),…

A: We have to find conditional distribution for given marginal PDFs.

Q: Choose two numbers, n¡ and n, randomly between 0 and 1000 and determine c 2) such that f(x) = cx…

A: Let n1=50 and n2=60. Then, to find c, use the condition of valid probability distribution function…

Q: The random variables X andY have joint cumulative distribution function = { x 0, y > 0 Fx,y(x, y)…

Q: 1) A continuous random variable, X, is described by the PDF shown below. It is input into a system…

A: Given that : A Continuous random variable x be described by the PDF shown below : it is input in a…

Q: 2. The probability density function of a random variable X on [2,5] is given by 1 f (x) = 1- Vx - 1…

Q: Let the combined density function of the two -dimensional continuous random variable (x, y) are p…

A: Solution: From the given information, joint density function of X and Y is

Q: Let Y be a continuous random variable with pdf .f(y)=2y, O b) V50 V30 2 V20 V5 3 V30

A: Using the given pdf, P(Y < b) is given by: And, P( Y > b) is given by:

Q: If the joint probability density function of two continuous random variables X and Y is given by…

A: Given Information: The joint probability density function of two continuous variables X and Y is:…

Q: Let X and Y be two continuous random variables having the joint pdf \[f(x,y) = \] Find the joint pdf…

Q: let x be a continuous random variable with probability density function Find ſb – 2x, 0<x < 2 1o.…

Q: Two continuous random variables Y₁ and Y₂ has the joint density function y2, if y₁>0, y2 > 0, y₁ +…

Q: 2) The joint probability density function of random variables X and Y is fx,(x,y) ={ fxy 0<r<1,…

A: NOTE: As per the guidelines, we are supposed to solve first three subparts only. Given: fX,Y(x,y)=xy…

Q: Let (X; Y ) be a continuous random vector with joint probability density function 0.5 -1sxs1,0sysl…

Q: Q1 Let X and Y be independent exponential random variables with rates A and u respectively where X>…

A: Given λ>μc>0 Find a and b

Q: 2. The continuous random variables X and Y have known joint probability density function 4x 0≤ y…

Q: Let Y1 and Y2 be two jointly continuous random variables with joint probability density function f…

A: Given the joint probability density function of continuous random variables Y1 and Y2 as fy1,…

Q: A3. Let X and Y be independent random variables with probability density functions fx(x) %3D e, >0…

Q: Let X and Y are two jointly distributed continuous random variable with probability density function…

A: From the given information, the joint density for X and Y is, fx,y=12, 0≤Y≤X, 0≤X≤2 a) Consider,…

Q: 4) The joint probability density function of two random variables is: fxy(x, y) = {c(1 + xy) 0 ≤ x ≤…

Q: Let the joint probability density function of continuous random variables X and Y be given by Find…

A: f(x,y)=2 ;0<x<y<10 otherwise The marginal PDF of Y is calculated as: f(y)=∫Range…

Q: Let X and Y are two jointly distributed continuous random variable with probability density function…

A: The joint probability density function of X and Y is: fx,y=12 if 0≤Y≤X and 0≤X≤20 otherwise (a)…

Q: Let X and Example 20. PDF 0<I<3, 0<yS3 fxy(r, y) = otherwise Find

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

Question

HW2: The joint probability density function of two discrete random variables X and
Y is given by p(x, y)=c(2x+y), where x and y can assume all integers such that 0<
xS 2, 0S y< 3, and p (x, y)= 0 otherwise. a) Find the value of the constant c. (c)
Find P(X >1, Y <2). (b) Find P(X =2, Y= 1).

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Multivariate Distributions and Functions of Random Variables$

Learn more about

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

Similar questions

X and Y are independent, X ~ U (0, 1) and Y U (0, 1). Calculate the probability P(X+Y<1.5).
The joint probability density function of X and Y is defined as f(r, y) = (1+2?)(1+y²) What is the probability that (X, Y) falls inside the square with vertices (0,0), (1,0), (1,1), and (0,1)? 16 O 1/2 O None of these. O 1/16
None
2. Let X and Y denote independent random variables with respective probability density func- tions fx(x) = 2x, 0
Q1. Random variables X and Y have joint Probability Density Function (PDF) fxx(x, y) = {2 - 1< x < y < 1 otherwises Find rx,y and E[e*+Y].
Let X and Y be two continuous random variables with joint pdf f(x, y) = cx²y(1+y) for 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3, and f(x, y) = 0 otherwise. (a) Find the value of c. (b) Find the probability P(1 ≤ X ≤ 2, 0 ≤ Y ≤ 1). (c) Determine the joint cdf of X and Y for a and b between 0 and 3.
b) Let Y1, Y2.,Y5 be independent random variables with probability density function y 1 e 4 4 f(y)= ,y > 0 ,elsewhere 3 Determine the distribution and parameter of V = EY; using the method of moment i=1 generating function. Hence, find the mean of V using the moment generating function.
In Thunder Bay, during the month of June, afternoon thunderstorm rainfall frequently occurs. Based on the assumption that in Thunder Bay, there is a 20% chance of occurrence of a thunderstorm rainfall on any day of the month of June, compute the probability of having 5 days free of thunderstorm rainfall in Thunder Bay. What is the probability of one rainy day during the 5 days? (a) Compute the area under the standard normal curve for the following cases: (a) between z = 0 and z = 1.5, (b) z = -1.5 and z = 0, and (c) between z = - 0.5 and z= 2.5. (b) The probability of a flood event occurring every year is 0.4. What is the probability of this event occurring in year 2 and not in year 1? (c) What is the probability that a 5-year flood will occur three times in a period of 10 years? What is the probability that it will occur at all? How many floods of this magnitude will occur, on average, during the 10 years?
a) What is the value of k?