Suppose We Toss a Fair Coin Repeatedly

question 20

Multiple Choice

Suppose we toss a fair coin repeatedly. We continue to do this until a tail is observed. Let X be the number of tosses required. Then X has:

• A)a binomial distribution, with mean 0.5.
• B)a binomial distribution, with mean 2.
• C)a binomial distribution, with variance 0.707.
• D)None of the answer options is correct.

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Definitions:

Natural Log

The logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.71828.

Risk Averter

An individual or entity that prefers to avoid risk, typically choosing options with more certain outcomes over those with higher, but more uncertain, returns.

Expected Value

A calculated average of the possible outcomes of a given event, weighted by the likelihood of each outcome occurring.

Natural Log

The logarithm to the base \(e\) (where \(e\) is approximately 2.718), a constant used in mathematics and economics to model growth processes.