# Question about deriving probabilities in the Tobit model

In the Tobit model: Why do you divide by σ when deriving the probability that y = 0? Is it something to do with the assumption that ε is distributed N(0,σ^2) and not N(0,1)? If this is the case why does dividing by σ standardise it?

You’re correct - Dividing by $$\sigma$$ here makes it so that $$\epsilon/\sigma\sim N(0,1)$$. So now $$\phi$$ is the cdf of a standard normal random variable. Had the division not be made, it would be a normal random variable with variance $$\sigma^2$$. Dividing by $$\sigma$$ standardizes it because if $$X\sim N(0,\sigma^2),$$ $$var(X/\sigma)=\frac{1}{\sigma^2}var(X)=\sigma^2/\sigma^2=1.$$