Question 2 Let X1, X2, X3 be a random sample from a uniform distribution U(@ – ,0 + }). Consider the following estimators of 0: ô, - X, Ô2 = X(2)+ X(1) + X(3) where X is the sample mean, X(a), X(2), X(3) are the order statistics, that is, the smallest order statistic, the median, and the largest order statistic, respectively. (a) Show that 6, Ô2, and Ôg are unbiased estimators of 0. (b) Find var(0,), var(@2), and var(0,). (c) Compare the estimators. Which estimator would you prefer? Provide a reason.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
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