Let X_1,... be independent random variables with the common distribution function F, and suppose they are independent of N, a geometric random variable with parameter p. Let M=max(X_1,...,X_N). Find P(M le x) by conditioning on N.

s2vunov 2022-10-02 Answered
Conditional probability involving a geometric random variable
Let X 1 , . . . be independent random variables with the common distribution function F, and suppose they are independent of N, a geometric random variable with parameter p. Let M = m a x ( X 1 , . . . , X N ). Find P ( M x ) by conditioning on N.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Paige Paul
Answered 2022-10-03 Author has 11 answers
Step 1
The problem statement says that X 1 , X 2 , . . . all have the same distribution.
Now if I understand the problem statement correctly, you should find P ( M x ), however it seems to be easier to calculate P ( M x | N = k ) and then calculate P ( M x ).
Step 2
Note that: P ( M x ) = k = 1 P ( M x , N = k ) = k = 1 P ( N = k ) P ( M x | N = k )
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-10-30
Solving for the CDF of the Geometric Probability Distribution
Find the CDF of the Geometric distribution whose PMF is defined as P ( X = k ) = ( 1 p ) k 1 p where X is the number of trials up to and including the first success.
asked 2022-07-20
Geometric distribution and the probability of getting success at "first try"?
If one knows the probability of success p,
Then how does one calculate the probability of getting success at "first try" using geometric distribution?
Is it simply the probability of success? Are the successive events independent?
asked 2022-07-23
How to find sum of infinite geometric series with coefficient?
Given this series, p + p ( 1 p ) 3 + p ( 1 p ) 6 + p ( 1 p ) 9 + . . .
This is an infinite geometric series with ratio less than 1 since it's probability.
n = 0 p ( 1 p ) 3 n
Can you use geometric series sum formula? Is it p / ( 1 ( 1 p ) 3 )?
How do you deal with 3 that's in front of n?
asked 2022-09-23
Finding the probability distribution of the sum of geometric distributions?
X and Y are both geometric distributions with success p. What it the P r ( X + Y = n )
Would I use a convolution with a sum for this? Do I need to define a third random variable?
asked 2022-07-22
Geometric Probability Distribution, Expected Values
Let X Geometric ( θ ), and let Y = min ( X , 100 ). Compute (a) E(Y) and (b) E ( Y X ).
I know that the Geometric distribution is ( 1 θ ) k 1 θ and I also know how to calculate expected value but I'm confused about what it means that Y = min ( X , 100 )?
asked 2022-08-14
Find constant k with the probability mass function of a geometric series
Ok so I'm having some trouble getting this done. I think I've got the answer but I'm not really sure on how I could verify that the result I got is actually the correct answer.
So here's what the exercise says:
f ( x ) = k ( 1 5 ) 2 x + 3
where a discrete random variable X = 0 , 1 , 2 , 3 , . . . .
So I know this is a function for a geometric series given that the range for X is infinite.
Here's what I did:
1. i = 0 k ( 1 5 ) 2 x + 3 = 1
2. k 125 i = 0 ( 1 5 ) 2 x = 1
3. k 125 ( 1 1 1 5 ) = 1
4. k 125 ( 5 4 ) = 1
5. k 100 = 1
6. k = 100
So how do I know that is ok, I thought about using limits but I'm not sure if that is correct.
asked 2022-07-16
Probability of geometric Brownian motion
I want to solve the following question: Let X(t) be the price of JetCo stock at time t years from the present. Assume that X(t) is a geometric Brownian motion with zero drift and volatility σ = 0.4 / y r. If the current price of JetCo stock is 8.00 USD, what is the probability that the price will be at least 8.40 USD six months from now.
Here is my attempt: Since X(t) is a geometric Brownian motion, log(X(t)) is a regular Brownian motion with zero drift and σ = 0.4 / y r. We want to find the probability that log ( X ( 1 / 2 ) ) log ( 8.40 ) given that log ( X ( 0 ) ) = log ( 8.00 ).
What can I do from here?

New questions