- 6. Show that if E|X₁|' < ∞, j ≥ 2, then E|X₁ − µ|¹ ≤ 2¹ E|X₁|³. Hint: By the iterated expectation theorem - E|X₁ − µ|¹ = E{|X₁ − µ|³ ||X₁| ≥ |µ|}P(|X₁| ≥ |µ|) +E{|X₁ − µ|³ ||X₁| < |µ|}P(|X₁| < |µ|).

I chose option 1. I believe that the population mean number of times that adults eat fruit with their breakfast is greater than 3 times. I spoke with 14 adults and found that they had fruit with breakfast 7,2,3,0,0,0,4,7,7,7,4,4,5,and 0 times in the past week. Test this hypothesis at the .05 significance level and assume a random sample.