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**Danneedshelp** Q: Let $\displaystyle Y_{1},...,Y_{n}$ denote a random sample from the probability density function

$\displaystyle f(y|\theta)=\theta\\y^{\theta\\-1}$ for $\displaystyle 0<y<1$, $\displaystyle \theta>0$ and 0 otherwise.

a) Show that this density function is in the (one-parameter) exponential family and that $\displaystyle \sum_{i=1}^{n}-ln(Y_{i})$ is sufficient for $\displaystyle \theta$ (see previous exercise).

b) If $\displaystyle W_{i}=-ln(Y_{i})$, show that $\displaystyle W_{i}$ has an exponential distribution with mean $\displaystyle \frac{1}{\theta}$.

Previews exercise mentioned in (a):

1) Suppose that $\displaystyle Y_{1},...,Y_{n}$ is a random sample from a probability density in the (one-parameter) exponential family so that

$\displaystyle f(y|\theta)=a(\theta)b(y)e^{-[c(\theta)d(y)]}I_{[a,b]}(y)$, where $\displaystyle I_{[a,b]}(y)$ is the indicator function and a and b do not depend on $\displaystyle \theta$.

I think I am supposed to define each function in the density directly above for the orginal question; however, I am having a hard time doing so. Some direction would be great. Thanks.