Question: 12. Let {Xn} be a sequence of random variables. (a) If XnP0, then for any p>0 1+XnpXnpP0 and E(1+XnpXnp)0. (b) If for some p>0(6.21) holds,

12. Let {Xn} be a sequence of random variables. (a) If XnP0, then for any p>0 1+XnpXnpP0 and E(1+XnpXnp)0. (b) If for some p>0(6.21) holds, then XnP0. (c) Suppose p>0. Show XnP0 iff (6.22). 12. Let {Xn} be a sequence of random variables. (a) If XnP0, then for any p>0 1+XnpXnpP0 and E(1+XnpXnp)0. (b) If for some p>0(6.21) holds, then XnP0. (c) Suppose p>0. Show XnP0 iff (6.22)
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