) Determine the sampling distribution of the sample means obtained by tossing two dice
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My titleSuppose that you toss a pair of fair dice and write down the value of the top face from each die. That is, the value of the top face is a random variable.
- (a) What is the population distribution for one die? Write it out in a table.
- (b) Determine the sampling distribution of the sample means obtained by tossing two dice. Write it out in a table.
- (c) Calculate the variance of the sample mean, using the distribution of the population mean (Show your work!).
- (d) Calculate the variance of the sample mean, using the distribution of the sample mean (Show your work!). Comment.
X is normally distributed with X ∼ N (μX , 16) and Y is normally distributed independently from X , with Y ∼ N (1, 12). Let Z = X + 2Y .
- (a) What is the distribution of Z?
- (b) Say we observe a random sample of size 16 from Z, with a sample mean of Z = −4. Say the probability of observing a sample mean of at most −4 is 10%. What is μX ?
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