Covariance between ordinal variable and discrete variable

Question

I have two variables $y$ and $p$. Since $p$ is a discrete variable (numeric vector) and $y$ is an ordinal variable (total time watching TV).

  Values and categories of the variable y
  00 No time at all
  01 Less than 0,5 hour
  02 0,5 hour to 1 hour
  03 More than 1 hour, up to 1,5 hours
  04 More than 1,5 hours, up to 2 hours
  05 More than 2 hours, up to 2,5 hours
  06 More than 2,5 hours, up to 3 hours
  07 More than 3 hours

I want to calculate the covariance between $p$ and $y$ , so my questions are :

1. Is Kendall's Tau the advisable to calculate the correlation between $y$ and $p$ ?, or does it make sense if I categorize the vector $p$ according to intervals (convert it into ordinal data ) , then calculate Kendall's Tau correlation ?.
2. How can I calculate the variance of $y$ ?.