# Suppose that you toss a pair of fair dice and write down

Suppose that you toss a pair of fair dice and write down

Question
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.

1. (a) What is the population distribution for one die? Write it out in a table.
2. (b) Determine the sampling distribution of the sample means obtained by tossing two dice. Write it out in a table.
3. (c) Calculate the variance of the sample mean, using the distribution of the population mean (Show your work!).
4. (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 .

1. (a) What is the distribution of Z?
2. (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 ?

Suppose that you toss a pair of fair dice and write down

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