Answer the following questions with TRUE or FALSE, and explain your answer: (a) Let a random sample of independent X1 , . . . Xn be taken from a population with mean µx , variance σ2x . Then, the variance of X bar, (the sample mean) will always be less than or equal to the variance of X. (b) If X and Y have correlation 0.50, then the correlation
Answer the following questions with TRUE or FALSE, and explain your answer:
(a) Let a random sample of independent X1 , . . . Xn be taken from a population with mean µx , variance σ2x . Then, the variance of X bar, (the sample mean) will always be less than or equal to the variance of X.
(b) If X and Y have
(c) For n dependent random variables X1 , . . . , Xn , drawn from the same population with mean µx ,
E[X bar] = µx .
(d) If X has a variance of 4 and mean of 2, and a sample mean based on 4 independent Xi was
calculated, the probability that X will be larger than 8 is larger than the probability that X bar is
larger than 8.
***Note: (Please do not copy answer from Chegg!)
Hello! As you have posted 4 different questions, we are answering the first question. In case you require the unanswered question also, kindly re-post them as separate question.
a)
Given information:
Let a random sample of independent X1 , . . . Xn be taken from a population with mean µx , variance σ2x
From the central limit theorem,
The mean and variance of sample mean is,
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