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## Main Question or Discussion Point

If I have three scalar random variables: [itex]a[/itex], [itex]b[/itex] and [itex]c[/itex], which are each zero-mean and have some nonzero variances, and I know:

1) The correlation between [itex]a[/itex] and [itex]b[/itex] is nonzero.

2) The correlation between [itex]b[/itex] and [itex]c[/itex] is nonzero.

Does this imply that the correlation between [itex]a[/itex] and [itex]c[/itex] is nonzero?

I feel like the answer must be yes, but I don't have any sound mathematical reasoning for it. Any advice would be greatly appreciated!

1) The correlation between [itex]a[/itex] and [itex]b[/itex] is nonzero.

2) The correlation between [itex]b[/itex] and [itex]c[/itex] is nonzero.

Does this imply that the correlation between [itex]a[/itex] and [itex]c[/itex] is nonzero?

I feel like the answer must be yes, but I don't have any sound mathematical reasoning for it. Any advice would be greatly appreciated!