title: P(4 < X <12) using Chebyshev's not consistent with the simulation value
body: <p>On calculating P(4 &lt; X &lt; 12) using Chebyshev's with mean = 8 and variance = 7.9 the probability turned out to be 0.5 but when running this simulation in R I'm getting 0.79</p>
  <p>Is there something that I'm doing wrong?</p>
  <pre><code>nsims=10000
  x1=rpois(nsims,8)
  mean(x1)
  var(x1)
  length1 = length(which (x1 &lt; 12))
  length2 = length(which (x1 &lt;= 4))
  length1
  length2
  (length1 - length2)/nsims
  </code></pre>