Consider the Moment Generating Function (MGF) of the Binomial distribution Mx (t)((1 − p) + pet)n (p is the probability of success and n is the number of trials). Usingthe MGF derive E[X] and Var[X].=Consider random independent variables X₁, X₂, ... Xn which take 0 with the probability1 − p and 1 with the probability p.(a) Derive an expression for EXj[X](b) Find the Fisher's information I (p)

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Answered: Consider the Moment Generating Function…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.3: Binomial Probability

Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...

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Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.

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Consider the Moment Generating Function (MGF) of the Binomial distribution Mx(t) = ((1 − p) + pet)n (p is the probability of success and n is the number of trials). Using the MGF derive E[X] and Var[X].