Assume are independent , normal random variables where and for i = 1, 2, 3. For each of the following situations, use to construct a statistic with the indicated distribution. Briefly explain your...

1. Assume are independent , normal random variables where and for
   i
   = 1, 2, 3. For each of the following situations, use to construct a statistic with the indicated distribution.
   Briefly explain your reasoning in each situation.
   

1. (5 points) Standard Normal Distribution,
   

1. (5 points) Distribution with 2 degrees of freedom


2. (10 points) Distribution with 2 degrees of freedom

1. Assume 123 ,, XXX are independent , normal random variables where ( ) 2 i EXi = and ( ) 2 3 i VarXi = for i = 1, 2, 3. For each of the following situations, use 123 ,, XXX to construct a statistic with the indicated distribution. Briefly explain your reasoning in each situation. a) (5 points) Standard Normal Distribution, (0,1) N b) (5 points) 2 c Distribution with 2 degrees of freedom c) (10 points) t Distribution with 2 degrees of freedom _1420901968.unknown _1420901970.unknown _1420901972.unknown _1420901973.unknown _1420901971.unknown _1420901969.unknown _1420901967.unknown