Answered: Example 2.8. Let X and Y be jointly…

Example 2.8. Let X and Y be jointly continuous random variables with joint PDF is given by: fx,y (x, y) = 2 where 0 < y < x < 1 1. Show the marginal PDF of X and Y. 2. Find P(X >1/2).

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: Three research departments have 8, 7, and 6 members, respectively. Each department is to select a…

A: For Que 1: The first department has 7 choices for the delegate and then 6 choices for the alternate,…

Q: The joint density function of random variables X and Y is f(x, y). Find the mean and variance of the…

Q: Let X and Y be two independent continuous random variables with marginal distribution of X alone is…

A: Solution: From the given information, the marginal distributions of X and Y are

Q: Let X and Y denote two continuous random variables with the joint density function: f(r, y) = 0<<1,…

Q: Let the joint probability density function of random variables X and Y be defined as f(x, y) = {…

A: (a). Find the value constant c: The value of the constant c is obtained as 3/2 from the calculations…

Q: Let X and Y denote two contiuous random variables with the joint density function Įka 10, 0 <x< 1,…

A: The total area of the probability density function is equal to one. That is,

Q: Let X be a continuous random variable with cumulative distribution function I 27. Fx(1) =

A: 5. From the given information, Fx=0, x<1x3-12, 1≤x≤271 x>27 Consider, fx=ddxFx…

Q: Let X be a continuous random variable with a density function: |x| f(x) = - 2<x< 3 2 0, otherwise…

Q: X Let the probability density function of the random varibe be as follows o x>0, e>O %3D Firstly x…

Q: The random variable X has the density function: 1 f(x) = (9- x), 0sxs2 16 (a) The standard deviation…

A: The probability density function of a random variable X is given by fx. fx=1169-x, for 0≤x≤2. The…

Q: Functional form of the pdf f (x) for the gamma distribution for a continuous random variable X is f…

Q: Example 5-34: For each of the density functions of a continuous random variable X shown below, find…

Q: Let Xand Y be two continuous random variables with joint probability density 3x function given by:…

A: Compute the variance of 2X+Y using the formula: Var(2X+Y)=Var(2X)+Var(Y)+2Cov(2X,Y)…

Q: Question * Given the continuous random variables X and Y with joint probability density function: xy…

A: For the given, joint probability density function, we need to find the conditional probability:…

Q: Value of X Probability -7 -5 -3 -1 2 4 6 -2~2~2~2~2-2~2 1 12 12 12 12 12 1 12 12 What is the…

A: Given probability distribution of X is; Value of X Probability(P(X)) -7 1/12 -5 2/12 -3…

Q: Prove Theorem Let X be a random variable with the normal distribution S(x) = z ²] exp[=1/2(x– µ)²lo…

Q: b) Let U1, U2 be a random sample of size 2 from a uniform distribution over the interval (0, I). Let…

A: Let U1,U2 be a random sample from a uniform distribution (0.1) so the density function is given as…

Q: a passenger arriving at the Despin Spaceport must wait for a hotel shuttle is unformy between 3 and…

A: LetX: The amount of time a passenger arriving at the Bespin spaceport must wait for a hotel…

Q: Question * Let X be continuous random variable with probability density function given by: f(x) =…

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

A: We have given that f(x,y) = (1/16)x2e-x/2 x>0 0 elsewhere

Q: Let X and Y be two continuous random variables with joint density function: if0 <xSys2 f(x, y) 8…

Q: Write an expression for the joint density function.

Q: Let X and Y be two contimuous random variables with joint probability density function given by:…

A: Option B is the answer.

Q: Let the random variable Y be defined by Y = BX?,B > 0, where X is a continuous Rayleigh random…

A: The problem can be solved using the concept of pdf and random variables. please find step by step…

Q: نقطتان )2 Q7) A continuous random variable X has the following density function, find the expected…

A: Use expectation formula.

Q: Let X and Y be two continuous random variables with joint probability density function. 12 f(x, y)…

Q: The function that defines the probability distribution of a continuous random variable is a normal…

A: Given that, The function that defines the probability distribution of a continuous random variable.

Q: JA continuous random variable is uniformly distributed taking on values from 3 to 13. The density…

Q: Continuous random variables 2. Find the expected values of the continuous random variables with…

A: Solution-: We have, f(x)=1x2 for x≥1 =0 Otherwise We want to find E(X)=?

Q: Q5. Central limit theorem (Exponential distribution) Suppose X1,..., X„ are independent and…

A: Suppose X1,X2,....,Xn are samples from a distribution with a mean µ and standard deviation σ. Then,…

Q: Random variable X has a continous probbabilty distribution defined by distribution function:…

Q: Find Joint Density function of i-th & j-th order statistics in Uniform Distribution

A: From the general properties of order statistics, the joint density funtion of ith and jth order…

Q: Help

A: Uniform distribution:A random variable, say X ~ U(0,1) is said to be standard uniform distribution…

Q: The joint density function for random variables X and Y is f(x, y). Find the conditional mean and…

Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

Joint and Marginal Density Function for Continuous Random Variables

Example 2.8. Let X and Y be jointly continuous random variables with joint PDF is given by:
fx.y (x, y) = 2 where 0< y < x <1
1. Show the marginal PDF of X and Y.
2. Find P(X > 1/2).

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Continuous Probability Distribution$

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

Question * Let X be a continuous random variable with a density function: {: 3|x| k 2 - 2
Proof that a beta distribution with parameters alpha equal beta equal four is symmetric at its mode
7let x continuous random Variable ea Probabil;ty density function fx (X), The firobability distribution of a random Variable Y= ax+b (azo, b fixed)is: it has is 2. 3-
A random variable is normally distributed with a mean of 90 and a standard deviation of a = 5. (a) The following figure shows that the normal curve almost touches the horizontal axis at three standard deviations below and at three standard deviations above the mean (in this case at 75 and 105). Areas Under the Curve for any Normal Distribution 99.7% 95.4% 68.3% O R μ-30 80 Sketch a normal curve for the probability density function. Label the horizontal axis with values of 75, 80, 85, 90, 95, 100, and 105. 20 12 A-lo # μ+10 95 105 100 90 80 # +30 μ + 20 90 100 105 95 85 75 6 105 100 95 75 80 85 90 8 80 75 95 100 105 (b) What is the probability the random variable will assume a value between 80 and 100? (Round your answer to three decimal places.) (c) What is the probability the random variable will assume a value between 75 and 105? (Round your answer to three decimal places.)
Marginal distribution of x,that is fX(x)
Question * Let X and Y be two continuous random variables with joint probability density function given by: (х. у)%3D (8xy, 0
CORRECT AND DETAILED ANSWER
Question * Let X and Y be two continuous random variables with joint probability density (3x function given by: f(x.y)%= 0sysrsl elsewhere 3. E(X')= 3. 3. with E(X) E(Y) = 2, E(Y') = and E(XY)= 10 Then the value of the varianee of X+Y IS. 91/320 3/80 43/320 7/20