Find P[X>Y | X<2Y] of iid variables

  • Thread starter Thread starter jenuine
  • Start date Start date
  • Tags Tags
    Variables
Click For Summary
SUMMARY

The discussion focuses on calculating the conditional probability P[X>Y | X<2Y] for independent exponentially distributed random variables X and Y, each with a mean of 1. Participants emphasize the importance of using conditional probability and suggest sketching the relevant regions on the xy-plane to visualize the integration process. The need for clarity in explaining attempted methods is highlighted, as it aids in collaborative problem-solving.

PREREQUISITES
  • Understanding of conditional probability
  • Familiarity with exponential distributions
  • Basic knowledge of integration techniques
  • Ability to interpret graphical representations of probability
NEXT STEPS
  • Study the properties of independent exponential random variables
  • Learn techniques for calculating conditional probabilities
  • Explore integration methods for probability density functions
  • Practice sketching probability regions in the xy-plane
USEFUL FOR

Statisticians, data scientists, and students studying probability theory who are looking to deepen their understanding of conditional probabilities involving exponential distributions.

jenuine
Messages
5
Reaction score
0
Let X and Y be independent exponentially distributed random variables, each with mean 1. Find P[X>Y|X<2Y]






I know I must use conditional probability, but I can't simplify it enough to integrate.
 
Physics news on Phys.org


You need to show a bit more work. Keep in mind, we don't know you. None of us knows what you know and what you don't know. So even if what you've done so far seems trivial to you, you should explain what you've tried and where you're getting stuck.

For this problem, I suggest you sketch the regions of interest on the xy plane. That usually helps in seeing exactly what you need to integrate.
 

Similar threads

Find conditional probability mass function
  • · Replies 8 ·
Replies
8
Views
1K
What is the distribution of the sum of n iid Bernoulli random variables?
  • · Replies 1 ·
Replies
1
Views
1K
##\lim_{x \to0} \left(\dfrac{1}{\sin^2 x}-\dfrac{1}{x^2}\right)##
  • · Replies 5 ·
Replies
5
Views
2K
Getting the probability distribution of a random variable
  • · Replies 2 ·
Replies
2
Views
1K
Determine whether ## S[y] ## has a maximum or a minimum
  • · Replies 18 ·
Replies
18
Views
3K
How should I calculate the stationary value of ## S[y] ##?
  • · Replies 2 ·
Replies
2
Views
2K
Find the constrained maxima and minima of ##f(x,y,z)=x+y^2+2z##
  • · Replies 2 ·
Replies
2
Views
2K
Determine marginal densities and distributions from joint density
  • · Replies 7 ·
Replies
7
Views
1K
Finding Probability Density Functions for Independent Random Variables
  • · Replies 2 ·
Replies
2
Views
2K
Find the second derivative of the relation; ##x^2+y^4=10##
  • · Replies 24 ·
Replies
24
Views
3K