Find the sample mean and variance

4. Suppose X has mean a and variance o'. For each of the following give the mean and variance. (a) Y = (X - p); (b) Y = X/o; (c) Y = (X -p)/o. 5. Let X be the mean of a random sample of size 100 from a random variable that is distributed with mean 200, variance 400, and a distribution that is not the normal distribution. (a) Give the mean of X. 54 CHAPTER 3. @ A. COLIN CAMERON: THE SAMPLE MEAN (b) Give the variance and standard deviation of X. (c) Is X likely to be approximately normally distributed? Explain