Let x1, x2, , xn be a random sample of size n from the exponential distribution whose pdf is f(x; θ) = (1/θ)e−x/θ , 0 < x < [infinity], 0 < θ< [infinity].(a) show that x is an unbiased estimator of θ.(b) show that the variance of x is θ 2/n.(c) what is a good estimate of θ if a random sample of size 5 yielded the sample values 3.5, 8.1, 0.9, 4.4, and 0.5?

the answer

b. they are parallel and will never intersect.

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation:

linear pair postulates