Question

X = \begin{cases} a & \text{with probability } 1/2, \\ b & \text{with probability } 1/4, \\ c & \text{with probability } 1/8, \\ d & \text{with probability } 1/8. \end{cases}

          X = \begin{cases} a & \text{with probability } 1/2, \\ b & \text{with probability } 1/4, \\ c & \text{with probability } 1/8, \\ d & \text{with probability } 1/8. \end{cases}

X = a with probability 1/2,
b with probability 1/4,
c with probability 1/8,
d with probability 1/8.

Added by Christina H.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

Instant Answer

Solved by Expert Danielle Ashley

Step 1

The entropy of a fair coin can be calculated using the formula for entropy: H(X) = -Σ p(x) log2 p(x), where p(x) is the probability of each outcome. In this case, there are two outcomes (heads and tails) with equal probabilities of 0.5. So, the entropy of a fair Show more…

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a. What is the entropy of a fair coin? Hint: Two classes, p(x) = 0.5 for each. b. What is the entropy of a fair dice? c. A random variable is defined as: What is its entropy? Would the value be greater or smaller if all the values had an equal probability? d. For a two-class mixture, when is the value of entropy maximized? What about an "n-class" mixture? with probability 1/2, with probability 1/4, with probability 1/8, with probability 1/8. b X = c d