1. Use the Neymann-Pearson lemma to develop a best test for Ho: B= 6 versus Ha:ß=4 for the exponential pdf with mean ß. f(x)=1/B exB x>0_Assume n=6 Find the rejection region for a=0.05 |

You are performing a two-tailed z-test If a = 0.2, find the positive critical value, to two decimal places.

Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.

10.  You estimated a regression with the following output.         Source |       SS           df       MS      Number of obs   =       333 -------------+----------------------------------   F(1, 331)       =   4608.21        Model |  32636494.1         1  32636494.1   Prob > F        =    0.0000     Residual |   2344225.8       331  7082.25316   R-squared       =    0.9330 -------------+----------------------------------   Adj R-squared   =    0.9328        Total |  34980719.9       332  105363.614   Root MSE        =    84.156   ------------------------------------------------------------------------------            Y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval] -------------+----------------------------------------------------------------            X |   30.79902   .4537022    67.88   0.000     29.90652    31.69153        _cons |   20.85313    42.1964     0.49   0.621     -62.1538    103.8601…

when using delta method to calculate variance, shouldn't [g'(μ)]^2 equal to (θ+1)^4?

Solve with R, please

Let Y be a random variable with the mgfM(t) = .35e^(−4t) + .1 + .25e^(2t) + .3e^(4t).(a) What is the pmf of Y?(b) Calculate the variance of Y directly from the pmf you determined in part (a).(c) Calculate E[Y^4] directly from the mgf.