Power function (statistics)

[sara_87]

A coin is suspected of bias towards heads, so a test is made of the hypothesis H0: p=2 against H1:p>2, where p is the probability of heads. The test is to count the number of heads, X, in 10 tosses of the coin, and reject H0 if X=8, 9, or 10.
Show that the power function for this test is given by: p^8(45-80p+36p^2)

I have no idea how to start. I know that the power function means: P(reject H0 given H0 is false) but i don't know how to continue.

Any help would be very much appreciated.
Thank you

 

[Nino MMP]

.The power function for this test is given by the probability of getting 8, 9, or 10 heads in 10 tosses of the coin, given that the true probability of heads is greater than 2. That probability can be calculated using the binomial distribution as:P(X=8,9,10) = P(X=8) + P(X=9) + P(X=10) = C(10,8) * p^8 * (1-p)^2 + C(10,9) * p^9 * (1-p)^1 + C(10,10) * p^10 * (1-p)^0 = 10 * p^8 * (1-p)^2 + 10 * p^9 * (1-p) + p^10 = 10p^8 - 80p^9 + 36p^10 + p^10 = p^8(45 - 80p + 36p^2).