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2.6-5. Let the moment-generating function M(t) of X exist for hth. Consider the function R(t)= lnM(t) . The first two derivatives of R(t) are, respectively, R(t)=M(t)M(t) and R(t)=[M(t)]2M(t)M(t)[M(t)]2. Setting t=0,2 show that (a) =R(0). (b) 2R(0). 2.6-6. Use the result of Exercise 2.6-5 to find the mean and variance of the (a) Bernoulli distribution. (b) Binomial distribution. (c) Geometric distribution..

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2.6-5. Let the moment-generating function M(t) of X exist for hth. Consider the function R(t)= lnM(t) . The first two derivatives of R(t) are, respectively, R(t)=M(t)M(t) and R(t)=[M(t)]2M(t)M(t)[M(t)]2. Setting t=0,2 show that (a) =R(0). (b) 2R(0). 2.6-6. Use the result of Exercise 2.6-5 to find the mean and variance of the (a) Bernoulli distribution. (b) Binomial distribution. (c) Geometric distribution.

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265 Let the momentgenerating function Mt of X exist fo.pdf

  • 1. 2.6-5. Let the moment-generating function M(t) of X exist for hth. Consider the function R(t)= lnM(t) . The first two derivatives of R(t) are, respectively, R(t)=M(t)M(t) and R(t)=[M(t)]2M(t)M(t)[M(t)]2. Setting t=0,2 show that (a) =R(0). (b) 2R(0). 2.6-6. Use the result of Exercise 2.6-5 to find the mean and variance of the (a) Bernoulli distribution. (b) Binomial distribution. (c) Geometric distribution.