Which of the Following Statements Are True If $X _ { 1 } , X _ { 2 } , \cdots \cdots , X _ { n }$

question 22

Multiple Choice

Which of the following statements are true if $X _ { 1 } , X _ { 2 } , \cdots \cdots , X _ { n }$ is a random sample from a distribution with mean $\mu$ ?

• A) The sample mean \(\bar { X }\)
• Is always an unbiased estimator of \(\mu\)
• )
• B) The sample mean \(\tilde { \mu }\)
• Is an unbiased estimator of \(\mu\)
• If the distribution is continuous and symmetric.
• C) Any trimmed mean is an unbiased estimator of \(\mu\)
• If the distribution is continuous and symmetric.
• D) None of the above statements are true.
• E) All of the above statements are true.

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Definitions:

Batesian Mimicry

A form of mimicry where a harmless species evolves to imitate the warning signals of a harmful species to deter predators.

Poison Arrow Frog

A group of brightly colored frogs, native to tropical Central and South America, known for the potent toxin secreted through their skin.

Chemical Defenses

Strategies involving the production of chemical substances by organisms to deter predation, infection, or competition.

Mutualism

A type of symbiotic relationship between two species where both parties benefit from the interaction.