The lower and upper bound for the 11 numbers that should be chosen where the 11 numbers include the lower and upper bounds is given as 37 through 63.
Expectation Value :
In an experiment, the expected value is what you expect to observe if the experiment is replicated many times. Additionally, the observed value may not be exactly equal to the expected value, but it's likely to be fairly close, either a little above or a little below.
According to the given condition,A coin will be tossed 100 times. You get to pick 11 numbers. If the number of heads turns out to equal one of your 11 numbers, you win a dollar.Therefore, the probability of getting a head in a single coin toss is 0.5, and the probability of getting a tail in a single coin toss is 0.5.So, the expected number of heads in 100 tosses will be 100 × 0.5 = 50.Then, we need to look for a range of numbers that can result in 50. In this regard, we have to break this 50 number down into some smaller ones that add up to 50:49 + 1, 48 + 2, 47 + 3, 46 + 4 and so on.In each sum, the first number represents the number of tails, while the second number represents the number of heads. For example, 49 + 1 means that the number of tails is 49, and the number of heads is 1. We only need to find the 11 sums with at least one of the numbers from 37 to 63.So, the 11 numbers you pick go from a lower bound of 37 through an upper bound of 63.