Let x represent a binomial random variable with parameters n and p. Show that (a) E(x) : = n(n − 1)p²; (c) E[x(x - 1)(x − 2)] mp; (b) E[x(x − 1)] - = - - 1)(n − 2)p³; -
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![5-25 Let x represent a binomial random variable with parameters n and p. Show that (a) E(x) =
n(n − 1)p²; (c) E[x(x − 1)(x − 2)]
-
=
n(n − 1)(n − 2)p³;
np; (b) E[x(x − 1)]
(d) Compute E (x²) and E(x³).
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb111e67b-7fa2-4f53-8212-b6251b681bde%2Fc6992e01-678d-4933-8bac-6c04ca2f4276%2Fggj3hc_processed.jpeg&w=3840&q=75)
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- The moment generating function of the random variable X is given by mx(s) = e2e-2 and the moment generating function of the random variable Y is my (s) = (et + )10. If it is assumed that the random variables X and Y are independent, find the following: (a) E(XY); (b) E[(X – Y)²] (c) Var(2X – 3Y).1 If X and Y are independent random variables, show that E [XY] = E[X] E[Y] E [g1(X) g2(X)] = E [g1 (X)] E [g2 (X)1 andLet X be a random variable. Find E(Y) where 3 Y = (X – E(X)) (a) 1 (d) 0 (c) -3/4 (b) 3/4 (е) —1 -
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