please help?do 1,3,4

Sampling from N(1, (2) Do 1, 3 (nandc), 4 . 16: 02= 1 Hair = 4 m = 5 = 05 Develop best test 2. A single observation of a random variable having an exponential distribution is used to test the null hypothesis that the mean of the distribution is 0 = 2 against the alternative that it is 0 =5. If the null hypothesis is accepted if and only if the observed value of the random variable is less than 3, find the probabilities of type I and type II errors. 3. . Let X1,..X, denote a random sample from a normal N(0,25) distribution. Show that the best critical region for testing H. : 0 =5 vs. Ha : 0 =7 is C = {(x1,...,Xn) : x 2 c}. Find n and c so that P( X Z C; H.)=.05 P( X Z C; Ha) =.80 Find a UMP test, if one exists for testing Ho: M=2 versus Ha: 1