Let š be a standard normal random variable
LetĀ šĀ be a standard normal random variable. Another random variable is determined as follows. We flip a fair coin (independent fromĀ š). In case of Heads, we letĀ š=š. In case of Tails, we letĀ š=āš.
Ā
IsĀ šĀ normal?
Ā
yes
Ā
Ā no
Ā
Ā not enough information to determine
Ā
ComputeĀ cšš(š,š).
Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā cšš(š,š) = ?
Ā Ā
AreĀ šĀ andĀ šĀ independent?
Ā
Ā yes
Ā
Ā no
Ā
Ā not enough information to determine
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Let š be a standard normal random variable.
LetĀ šĀ be a standard normal random variable. Another random variable is determined as follows. We flip a fair coin (independent fromĀ š). In case of Heads, we letĀ š=š. In case of Tails, we letĀ š=āš.Ā IsĀ šĀ normal?Ā Ā - yesĀ Ā - noĀ Ā - not enough information to determineĀ ComputeĀ cšš(š,š).Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā cšš(š,š) = ?AreĀ šĀ andĀ šĀ independent?Ā Ā - yesĀ Ā - noĀ Ā - not enough information to determine
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