[amp_mcq option1=”0″ option2=”1″ option3=”Infinite” option4=”Cannot be determined” correct=”option1″]<\/p>\n
The correct answer is: A. 0<\/p>\n
Entropy is a measure of the uncertainty associated with a random variable. A random variable is a variable whose value is uncertain. The entropy of a random variable is a measure of how much information is needed to specify the value of the variable.<\/p>\n
The entropy of a random variable can be calculated using the following formula:<\/p>\n
$H(X) = -\\sum_{x \\in \\mathcal{X}} p(x) \\log p(x)$<\/p>\n
where $p(x)$ is the probability of the random variable taking on the value $x$.<\/p>\n
If the random variable is certain, then the entropy is zero. This is because there is no uncertainty in the value of the variable, so no information is needed to specify it.<\/p>\n
If the random variable is completely random, then the entropy is one. This is because there is maximum uncertainty in the value of the variable, so the maximum amount of information is needed to specify it.<\/p>\n
In general, the entropy of a random variable will be between zero and one. The closer the entropy is to zero, the more certain the random variable is. The closer the entropy is to one, the more random the random variable is.<\/p>\n
In the case of the question, the random variable is a coin toss. The possible values of the random variable are heads and tails. The probability of heads is $\\frac{1}{2}$ and the probability of tails is $\\frac{1}{2}$. Therefore, the entropy of the random variable is:<\/p>\n
$H(X) = -\\sum_{x \\in \\mathcal{X}} p(x) \\log p(x) = -\\frac{1}{2} \\log \\frac{1}{2} – \\frac{1}{2} \\log \\frac{1}{2} = 0$<\/p>\n
Therefore, the correct answer is A.<\/p>\n","protected":false},"excerpt":{"rendered":"
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