Let X be a discrete type random variable with PMF P(x; ) = x (1 )1x , x = 0,

Let X be a discrete type random variable with PMF P(x; θ ) =



θ x (1 − θ )1−x , x = 0, 1 0 otherwise .

We test the simple hypothesis H0 : θ = 1 4 against the alternative composite hypothesis H1 : θ < 1 4 by taking a random sample of size 10 and rejecting H0 if and only if the observed values x1, x2,..., x10 of the sample observations are such that 10 i=1 xi < 1. Find the power of this test.