Can you provide answers with bit explanation and how did you achieve this ?

Consider the Poisson regression model yi = Po (eoxi ). Write z = _i_1 Xiyi and di = exp (Oxi). (1) What is the expression for the log likelihood function, L (0)? O 20 + Eh- di O 20 - El-1 di O 20 - El-1 exp (di) (2) What is the first and second derivative of $L$, i.e. dL / de and d2 L/ de2? O L' (0) = En xiyi - EL xi exp (Oxi), L" (0) = - Ella, di O L' (0) = EL xiyi - Et, xi exp (Oxi) , L" (0) = - Exili O L' (0) = - En- Xi exp (Oxi) , L" (0) = - Ella, di O L' (0) = - EL-1 x; exp (Oxi), L" (0) = - Emaili(3) lfn = 10 and mi = 3 + (ii and z = 1551, what is the maximum likelihood estimator of 6? O 0.55 O 3.47 O 2.95 O 1.99 (4) What is the estimated variance of 0? 0 0.00045 0 0.17324 0 0.00023 O 0.00225 (5} What is the pvalue obtained for the test H0 : 0 = 2? (Use the 63 value rounded to two decimal places) 0 0.510 O 0.05 O 0.005 O 0.467