7. [Moment Generating Function] Derive the moment generating functions (MGF) of X ~ B(n, p) and Y ~ Poisson(A). Analyze if Mx(t) converges to My(t) when p→ 0, n→ ∞ and np → λ. Hint: for the latter question, use the following limit lim (1+ n→X n. n ex. 7. [Moment Generating Function] Derive the moment generating functions (MGF) of X ~ B(n, p) and Y ~ Poisson(A). Analyze if Mx(t) converges to My(t) when p→ 0, n→ ∞ and np → λ. Hint: for the latter question, use the following limit lim (1+ n→X n. n ex.
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- 9.) Consider the function f (x) = x? – 2x – 1 for x € [2,4]. Use n = 10 to compute accurate to 10 decimal places: a.) RHS b.) LHS c.) Midpoint Rule Sum d.) Find the error of RHS, LHS, (RHS + LHS) and the Midpoint Rule approximations7. Let f(t) be a function with the following graph. Let F(x) = S*, f (t) dt where -4Let a(t), 2 < t<8 be a positive function. Also, let the function 8(t) be defined as 8(t) = a'(t)/a(t) on the interval [2, 8]. Suppose that 8(t) 4/(t- 1), 2Recommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage