Final answer:
The reduced lottery is the simple lottery obtained by combining the probabilities of outcomes from a compound lottery.
For the given compound lottery L, the reduced lottery would be represented by the probabilities of obtaining each final outcome.
Step-by-step explanation:
The student is asking to find the reduced lottery corresponding to the compound lottery L = (L1, L2 ; π, 1 − π), where L1 = (1, 0), L2 = (τ, 1 − τ).
A compound lottery is a type of probability distribution in which the outcomes are other lotteries. We can 'reduce' this compound lottery to a simple one by calculating the probabilities of the final outcomes.
To reduce the compound lottery L, we combine the probabilities from L1 and L2 weighted by π and (1-π) respectively. The final outcomes are thus: getting 1 with probability π from L1 and getting τ with probability (1-π)*τ from L2. The other outcome from L2 is getting 1-τ with probability (1-π)*(1-τ).
The reduced lottery is then represented as follows: R = (1, τ, 1-τ; π, (1-π)*τ, (1-π)*(1-τ)). This gives us the simple lottery with each outcome and its corresponding probability.