Let Y1, Y2, . . . , Yn denote a random sample from a population having a Poisson distri- bution with mean λ. (a) Find the form of the rejection region for a most powerful test of H0 : λ = λ0 against Ha : λ = λa , where λa > λ0. (b) Recall that Pn i=1 Yi has a Poisson distribution with mean nλ. Indicate how this information can be used to find any constants associated with the rejection region derived in part (a).

Volume of cylinder(V) is given by:

           ....[1]

where, r is the radius of the cylinder and h is the height of the cylinder

From the diagram:

Diameter of a pipe (d) = 10 cm

height of the pipe(h) = 2m    

Use conversion:

1 m = 100 cm

then

2m  = 200 cm

⇒h = 200 cm

Since, a pipe is in the form of cylinder.

We have to find the volume of a pipe.

We know that:

⇒

Divide both sides by 2 we get;

5 = r

or

r = 5 cm

Substitute the given values and use  π = 3.14. in [1] we have;

Simplify:

Therefore, the volume of a pipe in cm³ is, 15700