Problem 1. A medical researcher is studying the risk of heart attack in men. She first divides men into three weight categories: thin, normal, and overweight. By studying the male ancestors, sons, and grandsons of these men, the researcher comes up with the following transition table: Current Step thin 0.3 thin normal 0.2 overweight 0.1 Next Step normal overweight 0.5 0.2 0.6 0.5 0.2 0.4 (a) Find the probability for a man of normal weight to have a thin son. How about thin grandson? Thin great-grandson? (b) Find the probability for an overweight man to have an overweight son. How about overweight grandson? overweight great-grandson? (c) Suppose that the distribution of men by weight is initially given by (0.2, 0.55, 0.25). Find the distribution after 1 generation. How about 2, or 3, generations? What is the long term prediction?

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