Let X 03 34 04 18 07 10 01 23 37 20 03 37 01 13 12 33 02 13

Let X : 0.3, 3.4, 0.4, 1.8, 0.7, 1.0, 0.1, 2.3, 3.7, 2.0, 0.3, 3.7, 0.1, 1.3, 1.2, 3.3, 0.2, 1.3, 0.6, 0.4. For the point estimate of the 20 observations, 1.405, find the estimated standard error. theta is an unknown parameter with the following 20 observations of where , = = 1,2,...,n be a random sample from an exponential distribution (population) with p.d.f. ,

Solution

Mean = 1.405 is the point estimate of the 20 observations

Variance of the sample is calculated as follows. E(X^2)-Mean^2

= 1.5055

Std deviation = rt of variance = 1.227

Std error = 1.227/rt n where n is the sample size

Here sample size = 20

Hence std error = 1.227/4.472 = 0.2744