how to get the probability of weighted sum of i.i.d random variables [on hold]Gaussian Distributed Random VariablesProbability Density Function of Difference of Minimum of Exponential VariablesFind the distribution of $overlineY$.convergence in law of Cauchy random variables.How do you show a sequence of random variable are not independent or identically distributed?Baye's rule application with multiple conditionsInequality involving the sum of normal random variablesSum of Random Variables i.i.d. with $mathbbE[|X_n|]=+infty$Sum of iid variables converge in probabilityFinding the distribution of a random variable
Do f-stop and exposure time perfectly cancel?
Low budget alien movie about the Earth being cooked
What Happens when Passenger Refuses to Fly Boeing 737 Max?
Is there a window switcher for GNOME that shows the actual window?
How could our ancestors have domesticated a solitary predator?
How to pass a string to a command that expects a file?
Why doesn't this Google Translate ad use the word "Translation" instead of "Translate"?
They call me Inspector Morse
Look through the portal of every day
Can someone explain what is being said here in color publishing in the American Mathematical Monthly?
How much attack damage does the AC boost from a shield prevent on average?
My story is written in English, but is set in my home country. What language should I use for the dialogue?
How strictly should I take "Candidates must be local"?
Force user to remove USB token
Fourth person (in Slavey language)
Why the color red for the Republican Party
A three room house but a three headED dog
Is having access to past exams cheating and, if yes, could it be proven just by a good grade?
Can you reject a postdoc offer after the PI has paid a large sum for flights/accommodation for your visit?
Unreachable code, but reachable with exception
How do I locate a classical quotation?
Space in array system equations
Offered promotion but I'm leaving. Should I tell?
Is "history" a male-biased word ("his+story")?
how to get the probability of weighted sum of i.i.d random variables [on hold]
Gaussian Distributed Random VariablesProbability Density Function of Difference of Minimum of Exponential VariablesFind the distribution of $overlineY$.convergence in law of Cauchy random variables.How do you show a sequence of random variable are not independent or identically distributed?Baye's rule application with multiple conditionsInequality involving the sum of normal random variablesSum of Random Variables i.i.d. with $mathbbE[|X_n|]=+infty$Sum of iid variables converge in probabilityFinding the distribution of a random variable
$begingroup$
Let $Y_1,Y_2,ldots$ be independent and identically distributed with $$mathbbP(Y_n=0) = alpha quad textand quad mathbbP(Y_n>y) = (1-alpha) e^-y, quad y>0.$$ Define random variables $X_n$, $n geq 0$, by $$X_0 := 0 qquad X_n+1 := alpha X_n + Y_n+1.$$ Prove that $$mathbbP(X_n=0) = alpha^n quad textand quad mathbbP(X_n>x) = (1-alpha^n) e^-x, quad x>0.$$
probability
edited 2 days ago
saz
81.7k861127
asked 2 days ago
hungry manhungry man
1
New contributor
hungry man is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
put on hold as off-topic by Eevee Trainer, saz, Cesareo, mrtaurho, Davide Giraudo 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, saz, Cesareo, mrtaurho, Davide Giraudo
add a comment |
$begingroup$
Let $Y_1,Y_2,ldots$ be independent and identically distributed with $$mathbbP(Y_n=0) = alpha quad textand quad mathbbP(Y_n>y) = (1-alpha) e^-y, quad y>0.$$ Define random variables $X_n$, $n geq 0$, by $$X_0 := 0 qquad X_n+1 := alpha X_n + Y_n+1.$$ Prove that $$mathbbP(X_n=0) = alpha^n quad textand quad mathbbP(X_n>x) = (1-alpha^n) e^-x, quad x>0.$$
probability
edited 2 days ago
saz
81.7k861127
asked 2 days ago
hungry manhungry man
1
New contributor
hungry man is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
put on hold as off-topic by Eevee Trainer, saz, Cesareo, mrtaurho, Davide Giraudo 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, saz, Cesareo, mrtaurho, Davide Giraudo
$begingroup$
The problem is in that link
$endgroup$
– hungry man
2 days ago
$begingroup$
We cannot help you to solve this problem unless you add some of your own thoughts to the question. What have you tried? What e.g. about computing $P(X_n=0)$? Please use Mathjax in future.
$endgroup$
– saz
2 days ago
add a comment |
$begingroup$
Let $Y_1,Y_2,ldots$ be independent and identically distributed with $$mathbbP(Y_n=0) = alpha quad textand quad mathbbP(Y_n>y) = (1-alpha) e^-y, quad y>0.$$ Define random variables $X_n$, $n geq 0$, by $$X_0 := 0 qquad X_n+1 := alpha X_n + Y_n+1.$$ Prove that $$mathbbP(X_n=0) = alpha^n quad textand quad mathbbP(X_n>x) = (1-alpha^n) e^-x, quad x>0.$$
probability
edited 2 days ago
saz
81.7k861127
asked 2 days ago
hungry manhungry man
1
New contributor
hungry man is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Let $Y_1,Y_2,ldots$ be independent and identically distributed with $$mathbbP(Y_n=0) = alpha quad textand quad mathbbP(Y_n>y) = (1-alpha) e^-y, quad y>0.$$ Define random variables $X_n$, $n geq 0$, by $$X_0 := 0 qquad X_n+1 := alpha X_n + Y_n+1.$$ Prove that $$mathbbP(X_n=0) = alpha^n quad textand quad mathbbP(X_n>x) = (1-alpha^n) e^-x, quad x>0.$$
probability
probability
edited 2 days ago
saz
81.7k861127
asked 2 days ago
hungry manhungry man
1
New contributor
hungry man is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
saz
81.7k861127
asked 2 days ago
hungry manhungry man
1
New contributor
hungry man is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
saz
81.7k861127
edited 2 days ago
saz
81.7k861127
edited 2 days ago
saz
81.7k861127
81.7k861127
asked 2 days ago
hungry manhungry man
1
New contributor
hungry man is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
hungry manhungry man
1
asked 2 days ago
hungry manhungry man
1
1
New contributor
hungry man is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
hungry man is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
hungry man is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by Eevee Trainer, saz, Cesareo, mrtaurho, Davide Giraudo 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, saz, Cesareo, mrtaurho, Davide Giraudo
put on hold as off-topic by Eevee Trainer, saz, Cesareo, mrtaurho, Davide Giraudo 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, saz, Cesareo, mrtaurho, Davide Giraudo
$begingroup$
The problem is in that link
$endgroup$
– hungry man
2 days ago
$begingroup$
We cannot help you to solve this problem unless you add some of your own thoughts to the question. What have you tried? What e.g. about computing $P(X_n=0)$? Please use Mathjax in future.
$endgroup$
– saz
2 days ago
add a comment |
$begingroup$
The problem is in that link
$endgroup$
– hungry man
2 days ago
$begingroup$
We cannot help you to solve this problem unless you add some of your own thoughts to the question. What have you tried? What e.g. about computing $P(X_n=0)$? Please use Mathjax in future.
$endgroup$
– saz
2 days ago
$begingroup$
The problem is in that link
$endgroup$
– hungry man
2 days ago
$begingroup$
The problem is in that link
$endgroup$
– hungry man
2 days ago
$begingroup$
We cannot help you to solve this problem unless you add some of your own thoughts to the question. What have you tried? What e.g. about computing $P(X_n=0)$? Please use Mathjax in future.
$endgroup$
– saz
2 days ago
$begingroup$
We cannot help you to solve this problem unless you add some of your own thoughts to the question. What have you tried? What e.g. about computing $P(X_n=0)$? Please use Mathjax in future.
$endgroup$
– saz
2 days ago
add a comment |
0
active
oldest
votes
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The problem is in that link
$endgroup$
– hungry man
2 days ago
$begingroup$
We cannot help you to solve this problem unless you add some of your own thoughts to the question. What have you tried? What e.g. about computing $P(X_n=0)$? Please use Mathjax in future.
$endgroup$
– saz
2 days ago