Let X1 and X2 be independent chi-square random variables with r1 and r2 degrees of freedom, respectively. Let Y1 = (X1/r1)/(X2/r2) and Y2 = X2. (a) Find the joint pdf of Y1 and Y2. (b) Determine the marginal pdf of Y1 and show that Y1 has an F distribution. (This is another, but equivalent, way of finding the pdf of F.)

Statistical Inference: provides methods for drawing conclusions about a population from the sample data. There are two ways to do this: Confidence intervals: used to estimate the value of a population parameter using sample statistics Test of Significance: used for assessing evidence for a claim about the population To set up Have to have an SRS from the population, no bias The variable has to have an exactly normal distribution in the population We don’t know population mean , but we know the population standard deviation Confidence Interval What statistic can be used to estimate the population parameter o We can use x-bar To do a confidence interval, it is similar to the 68-95-99.7