If o(t) is the real valued characteristic function of a r.v. X, then prove that : (ii) 1 + $(20) ≥ 2 [(e)]² (1) 1-4 (20) ≤4 [1-(0)]; av

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Q: 5 Refer to the figure to determine each of the following: Exercise 5 y y = f(x) (2, 4) (1, 2) (a)…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 12. Examine the validity of the mean value theorem for: a) f(x) = lx² + mx + n in [a,b]

A: Consider the function fx=lx2+mx+n in a,b Here, the objective is to examine the validity of the mean…

Q: 8. (13 points) Define f: ZZ by f(n) = 5n - 5 for all integers n (a) Is one to one? Prove or give a…

A: Step 1:Step 2: Step 3: Step 4:

Q: 2. (a) Let A = {x = [0, 1]: x has a decimal representation not containing the digit 5.} Show that A…

A: We shall use certain results from measure theory

Q: 6. (a) Use the Schröder-Bernstein Theorem to prove that [a, b]| = |(a,b)| for any a, b e R. (b) Use…

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Q: A researcher wanted to determine if carpeted rooms contain more bacteria than uncarpeted rooms. The…

A: Given :

Q: Prove that x² +¸µ111² +21112 where prime denotes differentiation w.r.t.s. = 1 o² + 1+p¹² P

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Q: Q2\A\ Which of the following functions are bijective 2- f: R{0}→ R\{0},f(x) = 1/x این 2- f:R→R,f(x)…

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Q: 9. (a) Verify that the function satisfies the hypotheses of Rolle's Theorem and find all values of c…

A: We have to verify the Rolle's theorem and use the Mean value theorem.

Q: Suppose f: R → R is defined by the property that f(x) = x + x² + x³ for every real number x, and g:…

A: We are given that, for all real number x,          f(x) = x + x2 + x3  And        (g o f)(x) = x…

Q: that satisfy f(x) = x³ + x – 1, [0,2]

A: Note:- Since you have asked multiple questions, we will solve the first question for you. If you…

Q: Let f1, f2, .. fn be n real-valued, differentiable functions.- Prove that e :[fif2 ... fn] = (fif2…

A: We have to prove that the given formula.

Q: 1. Let N = {1, 2, 3,...} and let f: N→ N be a function given by f(x) = 2x + 3. (i) Find f(f(4) + 1).…

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Q: . There is a function f that's continuous at 0 and f(x) = f(2x) for all x's please show that f must…

A: Answer for sub question 1a: First step is to show fx=f2-nx for each integer n≥0. If n=0: fx=f2-0x…

Q: LET • (CX)= In [x²(x+5) ³ (x² + 4)⁰7 f'(x) = LET F(x) = \n [X²(X + 3) ³ (X² + 2)²] Cico

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Q: What conditions are necessary in order to use the dependent samples t​-test for the mean of the…

A: Necessary conditions for dependent samples in t-test, and for the difference in the means of two…

Q: Given the function g(x) 1 show that for the interval (2, 6) there exists no real number X – 4' c…

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Q: Let f(9) - 3 and f'(x) > 1 for 9 1 , we have f(11) > : this the smallest f(11) can be.

A: So, in our case , there must exist a c for which this holds true for 9<=x<=11

Q: coth- x = In () Q1/ Prove that

A: To prove coth-1x=(1/2)ln[(x+1)/(x-1)]

Q: a) Are the body mass leanness and heat-loss ratecorrelated? Explain your reasoning.   b) Calculate…

A: Given  X¯=3.96667, Y¯=0.04833 ∑Xi-X¯2=41.14667              ∑Yi-Y¯2=0.01696…