tWIce, • A : the first toss is heads. • B: the second toss is heads. • C: both tosses are the same. ow that A and B are independent. Show that A and C are independent. Show that B and C are dependent. Finally, show that A, B, and C are not mutually independent.

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This is a Statistics problem. Please explain each step thoroughly. 

The problem I'm having issues with is shown below:

In an experiment where you toss a fair coin twice, define events:

  • AA : the first toss is heads.
  • BB : the second toss is heads.
  • CC : both tosses are the same.

Show that AA and BB are independent. Show that AA and CC are independent. Show that BB and CC are independent. Finally, show that AA, BB, and CC are not mutually independent.

In an experiment where you toss a fair coin twice, define events:
• A: the first toss is heads.
• B: the second toss is heads.
• C: both tosses are the same.
Show that A and B are independent. Show that A and C are independent. Show that B and C are
independent. Finally, show that A, B, and C are not mutually independent.
Transcribed Image Text:In an experiment where you toss a fair coin twice, define events: • A: the first toss is heads. • B: the second toss is heads. • C: both tosses are the same. Show that A and B are independent. Show that A and C are independent. Show that B and C are independent. Finally, show that A, B, and C are not mutually independent.
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