Let x be a... a) Let x be a discrete random variable such that: P(x) = C(n, x) p* (1 – p)"- for all 0 0, εΖ. x! ed Use the fact that e to show that the expected value x= of x is equal to A. c) Let x...

Need to prove the following:

0, εΖ. x! ed Use the fact that e to show that the expected value x= of x is equal to A. c) Let x be a discrete random variable with expected value u. Show that (x – H)² = x(x – 1) + x – 2xµ + µ². d) Let x be a discrete random variable such that: P(x) = x! e for all x > 0, x E Z. Use the fact that e and that (x – µ)² = x(x – 1) +x – x! x=0 2.xu + µ? to show that the variance of x is equal to the expected value of x. "/>
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