Find approximately the least value of n

Reference no: EM131810249

Question: Let Xi be the last digit of D2i where Di is a random digit between 0 and 9. For instance, if D_i = 7 then D²_i = 49 and X_i = 9, Let X_n = (X₁ + .. X_n)/n be the average of a large number n of such last digits, obtained from independent random digits D₁, . .. D_n.

a) Predict the value of X_n for large n.

b) Find a number ? such that for n = 10,000 the chance that your predication is off by more than ? is about 1 in 200.

c) Find approximately the least value of n such that your prediction of X_n is correct to within 0.01 with probability at least 0.99.

d) Which can be predicted more accurately for large n: the value of X_n, or the value of D_n = (D₁ + . .. +D_n)/n?

e) If you just had to predict the first digit of X₁₀₀, what digit should you choose to maximize your chance of being correct, and what is that chance?

Reference no: EM131810249

Questions Cloud

Calculate the chance that your guess is correct : Calculate the chance that your guess is correct exactly for n = 1, 2, and approximately for a selection of larger values of n, and show the results in a graph.

Prepare a short report on a public project : Prepare a short report on a public project that summarizes the costs, benefits, disband fits, alternatives, and economic measures.

Budget request or funding authorization : Often, these are part of a budget request or funding authorization. These projects were (or could be) ranked how?

Finished goods costing to manufacture were sold on account : Finished goods costing $78,000 to manufacture were sold on account

Find approximately the least value of n : Let Xi be the last digit of D2i where Di is a random digit between 0 and 9. For instance, if Di = 7 then D2i = 49 and Xi = 9, Let Xn = (X1 + .. Xn)/n.

Expects an adjusted gross income : An unmarried taxpayer with no dependents expects an adjusted gross income of $70,000 in a given year. His nonbusiness deductions are expected to be $6000.

Compute the total tax : Compute the total tax they would pay as unmarried individuals. Then compute their tax as a married couple filing a joint return.

Prepare the journal entry to record the initial transaction : Prepare the journal entry (if one is required) to record the initial transaction and then prepare the adjusting entry.

Discuss what are the different classifications of accounts : What does the term account mean, What are the different classifications of accounts, How do the rules for debits and credits impact accounts

User Account

All Pages