2. (10%) Let X have an exponential distribution with mean θ > 0. Show that P(X > x + y | X > x) = P(X > y).

4. (10%) A die was cast $n = 120$ independent times and the following data resulted:If we use a chi-square test, for what values of b would the hypothesis that the die is unbiased be rejected at the 0.025 significance level? ($ \chi^2_{(5),\alpha=0.025} = 12.8 $; $ \chi^2_{(6),\alpha=0.025} = 14.4 $; $ \chi^2_{(5),\alpha=0.05} = 11.1 $; $ \chi^2_{(6),\alpha=0.05} = 12.6 $)