hi, does any one who can help me with these 4 econometric question?

Suppose you are employed by a large bank and you are currently studying which charac- teristics of borrowers and their loans are important for determining loan defaults. Con- sider the following latent variable model for loan defaults: y:=51+2X+31nZ+I34D+E With 8|X~N(0:02) Both X,- and Z, are continuous explanatory variables and D, is an indicator (dummy) variable that takes on only two valueszero or one. The 'observed' value of 3;, satises: _ 1 if y,\" > 0 gt 0 if y: S 0 Consider the Probit model which provides the following response probability: 1+I32X+a 1DZ+4DJ 0' Pr(y,- = me) = q>( where (EU represents the distribution (cumulative density) function for the standard normal distribution. a) [2 marks] 'The parameter 51 can be interpreted as the probability Pr[y = 1) when all the explanatory variables have a value of zero.' Explain whether this statement is true, false, or uncertain. b) [2 marks] 'The parameter [31 cannot be negative since probabilities must lie be- tween zero and one'. Explain whether this statement is true, false, or uncertain. c) [2 marks] Find the marginal effect of Z, on the response probability Pr(y, = 1|X,). d) [2 marks] Find the marginal effect of D,- on the response probability Pr(y, = 1|X,)