Suppose X is a random variable with mean µ. Suppose we observe X many times and keep track of the of the observed values. The law of large numbers says thatQuestion 10Answera.The value of µ will get larger and larger as we observe Xb.As we observe X more and more, this average and the value of µ will get larger and larger.c.As we observe X more and more, this average will get to be a larger and larger multiple of µ.d.This average will get closer and closer to µ as we observe X more and more oftene.All the above are true.

Which of the following best describes the Law of Large Numbers?As a coin is flipped a greater number of times, we would expect more heads than tails on average.We are more likely to roll a 3 or a 4 the more times we roll a dice.The average value of all of our dice rolls will converge upon 3.5 the more times we roll the dice.The more times we flip a coin, the more likely we are to predict which side it will land on.

Let X1, . . . , Xn are independent and identically distributed random variables with meanµ and variance σ2. Apply the result in Problem 4 for X = ∑ni=1 Xi/n to show the lawof large number

If random large samples of equal size are repeatedly drawn from any population, then the average of the mean of sample means will be approximately the same as the population mean.Question 9Select one:TrueFalse

According to the Central Limit Theorem, the sampling distribution of the sample mean becomes approximately normally distributed asthe standard error increasesthe population variance decreasesthe size of the population increasesthe number of  samples drawn increasesthe size of the sample increases

A random sample of size 50 is collected from a population 𝑃P, where 𝑃∼P∼ Uniform[0,12]. Find a lower bound on the probability that the sample mean will be at most 3 away from the actual mean using the weak law of large numbers. Enter the answer correct to three decimal places.