X*Z has same distribution of Y*Z? [closed]

XZ has same distribution of YZ? [closed]

Suppose I have three r.v.s $X, Y, Z$ such that $X$ and $Y$ are identically distributed.

Can we say that $Xcdot Z$ and $Ycdot Z$ have the same distribution? Can we prove it or disprove it?

Note: $X, Y, Z$ may be continuous r.v. and may be not necessarily be independent.

Thanks a lot in advance!

edited Dec 5 at 20:54

asked Dec 1 at 10:43

Giulio

273

closed as off-topic by amWhy, José Carlos Santos, user10354138, GNUSupporter 8964民主女神地下教會, Paul Frost Dec 1 at 11:31

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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, José Carlos Santos, user10354138, GNUSupporter 8964民主女神地下教會, Paul Frost

If this question can be reworded to fit the rules in the help center, please edit the question.

add a comment |

Suppose I have three r.v.s $X, Y, Z$ such that $X$ and $Y$ are identically distributed.

Can we say that $Xcdot Z$ and $Ycdot Z$ have the same distribution? Can we prove it or disprove it?

Note: $X, Y, Z$ may be continuous r.v. and may be not necessarily be independent.

Thanks a lot in advance!

edited Dec 5 at 20:54

asked Dec 1 at 10:43

Giulio

273

closed as off-topic by amWhy, José Carlos Santos, user10354138, GNUSupporter 8964民主女神地下教會, Paul Frost Dec 1 at 11:31

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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, José Carlos Santos, user10354138, GNUSupporter 8964民主女神地下教會, Paul Frost

If this question can be reworded to fit the rules in the help center, please edit the question.

add a comment |

Suppose I have three r.v.s $X, Y, Z$ such that $X$ and $Y$ are identically distributed.

Can we say that $Xcdot Z$ and $Ycdot Z$ have the same distribution? Can we prove it or disprove it?

Note: $X, Y, Z$ may be continuous r.v. and may be not necessarily be independent.

Thanks a lot in advance!

edited Dec 5 at 20:54

asked Dec 1 at 10:43

Giulio

273

Suppose I have three r.v.s $X, Y, Z$ such that $X$ and $Y$ are identically distributed.

Can we say that $Xcdot Z$ and $Ycdot Z$ have the same distribution? Can we prove it or disprove it?

Note: $X, Y, Z$ may be continuous r.v. and may be not necessarily be independent.

Thanks a lot in advance!

probability-theory

edited Dec 5 at 20:54

asked Dec 1 at 10:43

Giulio

273

edited Dec 5 at 20:54

asked Dec 1 at 10:43

Giulio

273

edited Dec 5 at 20:54

asked Dec 1 at 10:43

Giulio

273

asked Dec 1 at 10:43

Giulio

273

asked Dec 1 at 10:43

Giulio

273

closed as off-topic by amWhy, José Carlos Santos, user10354138, GNUSupporter 8964民主女神地下教會, Paul Frost Dec 1 at 11:31

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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, José Carlos Santos, user10354138, GNUSupporter 8964民主女神地下教會, Paul Frost

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by amWhy, José Carlos Santos, user10354138, GNUSupporter 8964民主女神地下教會, Paul Frost Dec 1 at 11:31

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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, José Carlos Santos, user10354138, GNUSupporter 8964民主女神地下教會, Paul Frost

If this question can be reworded to fit the rules in the help center, please edit the question.

add a comment |

1 Answer
1

active

oldest

votes

Clearly they can have the same distribution, for example if all three are independent. But they do not have to have the same distribution

For example, let $X=1$ or $-1$ each with probability $frac12$, $Y=-X$ and $Z=X$. All three have the same distribution. Then $XZ=1$ with probability $1$ while $YZ=-1$ with probability $1$, so these are different

answered Dec 1 at 10:52

Henry

98k475160

Thanks a lot! It's a clever answer to a question I didn't realise it was so trivial.
– Giulio
Dec 1 at 10:57

If they are independent, then they must have the same distribution. Is this what you mean?
– MPW
Dec 1 at 11:32

@MPW - yes, though are also other examples where $XZ$ and $YZ$ have the same distribution, such as $X=Y$
– Henry
Dec 1 at 17:05

add a comment |

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

Clearly they can have the same distribution, for example if all three are independent. But they do not have to have the same distribution

answered Dec 1 at 10:52

Henry

98k475160

Thanks a lot! It's a clever answer to a question I didn't realise it was so trivial.
– Giulio
Dec 1 at 10:57

If they are independent, then they must have the same distribution. Is this what you mean?
– MPW
Dec 1 at 11:32

@MPW - yes, though are also other examples where $XZ$ and $YZ$ have the same distribution, such as $X=Y$
– Henry
Dec 1 at 17:05

add a comment |

Clearly they can have the same distribution, for example if all three are independent. But they do not have to have the same distribution

answered Dec 1 at 10:52

Henry

98k475160

Thanks a lot! It's a clever answer to a question I didn't realise it was so trivial.
– Giulio
Dec 1 at 10:57

If they are independent, then they must have the same distribution. Is this what you mean?
– MPW
Dec 1 at 11:32

@MPW - yes, though are also other examples where $XZ$ and $YZ$ have the same distribution, such as $X=Y$
– Henry
Dec 1 at 17:05

add a comment |

Clearly they can have the same distribution, for example if all three are independent. But they do not have to have the same distribution

answered Dec 1 at 10:52

Henry

98k475160

Clearly they can have the same distribution, for example if all three are independent. But they do not have to have the same distribution

answered Dec 1 at 10:52

Henry

98k475160

answered Dec 1 at 10:52

Henry

98k475160

answered Dec 1 at 10:52

Henry

98k475160

answered Dec 1 at 10:52

Henry

98k475160

Thanks a lot! It's a clever answer to a question I didn't realise it was so trivial.
– Giulio
Dec 1 at 10:57

If they are independent, then they must have the same distribution. Is this what you mean?
– MPW
Dec 1 at 11:32

@MPW - yes, though are also other examples where $XZ$ and $YZ$ have the same distribution, such as $X=Y$
– Henry
Dec 1 at 17:05

add a comment |

Thanks a lot! It's a clever answer to a question I didn't realise it was so trivial.
– Giulio
Dec 1 at 10:57

If they are independent, then they must have the same distribution. Is this what you mean?
– MPW
Dec 1 at 11:32

@MPW - yes, though are also other examples where $XZ$ and $YZ$ have the same distribution, such as $X=Y$
– Henry
Dec 1 at 17:05

Thanks a lot! It's a clever answer to a question I didn't realise it was so trivial.
– Giulio
Dec 1 at 10:57

If they are independent, then they must have the same distribution. Is this what you mean?
– MPW
Dec 1 at 11:32

@MPW - yes, though are also other examples where $XZ$ and $YZ$ have the same distribution, such as $X=Y$
– Henry
Dec 1 at 17:05

add a comment |

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