Multiple choice. Circle all the correct answers a) You flip a coin 100,000 times and record the outcome in a random variable X such that Xi = 1 if…

Multiple choice. Circle all the correct answers 

a) You flip a coin 100,000 times and record the outcome in a random variable X such that Xi = 1 if the toss is “Heads” and 0 if its “Tails”. The Law of Large Numbers says that: 

i. It is impossible for the first n flips to all be “Heads” if n is large. 

ii. With high probability, the share of coin flips that are “Heads” will approximate 50%. 

iii. The sample mean of X is always 0.5 if the coin is fair, regardless of the number of times you flip the coin. 

iv. None of the above 

b. Which of the following statements are true: 

i. Type I error is the probability of rejecting the null when it is true 

ii. Type I error is the probability of not rejecting the null when it is true 

iii. Type II error is the probability of rejecting the null when it is false 

iv. Type II error is the probability of not rejecting the null when it is false 

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