Question

Imagine a situation in which there exist four possible outcomes: one with probability 1/6 one with probability 1/3 and two with probability 1/4 Calculate the diversity index. (Please round your answer to the hundredths place, i.e. 5.55). Enter only your final answer, and do not include anything else

Answer 1

The diversity index is calculated using the Shannon diversity index formula by summing the products of the probabilities and the natural logarithms of the probabilities for each possible outcome and then taking the negative of this sum.

Step-by-step explanation:

To calculate the diversity index when there are four possible outcomes with different probabilities, we need to apply the Shannon diversity index formula:

H' = -(Σ (p_i * log(p_i))), where p_i is the probability of each outcome.

For our case, we have the following probabilities for the four outcomes: 1/6, 1/3, 1/4, and 1/4. Plugging these into the formula gives:

H' = -((1/6 * log(1/6)) + (1/3 * log(1/3)) + (1/4 * log(1/4)) + (1/4 * log(1/4)))

By calculating each term and summing them, we will get the diversity index. It is important to use natural logarithms (base e) for the log function, and round off the final answer to the hundredths place to meet the requirement stated in the question.