Question

If your prediction for the total interval is realized in the first interval, what's your prediction for the remaining, solved using conditional expectation?

a) The same as the initial prediction
b) Zero
c) Double the initial prediction
d) Cannot be determined

Answer 1

If the total prediction is met in the first interval, the prediction for the remaining interval would be zero, based on conditional expectation.

Step-by-step explanation:

If your prediction for the total interval is realized in the first interval, your prediction for the remaining would be zero. This is because the prediction you made for the total has already been achieved, and so there is no additional amount expected in the remaining intervals. This concept is based on the idea of conditional expectation, where the remaining expectation is determined given that some conditions have been met.

Regarding the other parts of the question, which seem to relate to different probability and statistics scenarios, it is essential to define the random variable X in words, tailor the distribution used to the problem, and construct a confidence interval. For instance, constructing a 99 percent confidence interval for a mean includes stating the interval, sketching the graph, and calculating the error bound, which gives us an idea of how precise our estimate is. If we change the confidence level, the error bound changes as well because a higher confidence level means we need a wider interval to be more certain that it contains the true parameter.