The Euler's function ø(m) counts the number of integers a with 0 < a < m and gcd(a, m) = 1. (i) Let m = pª where p is prime. Show that (m) = m(1 – 1/p). (ii) Let m = pa and n = gb where p and q are distinct primes. Show that $(mn) = ¢(m)ø(n).

Q: Let Z~ of Z N(0,1). Find Pro.1 Select one: a. 0.81 Оъ -0.81 O c. -0.44 Od 044

A: We have given that  X~Normal(mean=0 , standard deviation=1) Find Z-score  P(Z&lt;z)=79.1%

Q: Let X Gamma(a, B). Prove that for any positive integer n > 1, E(X") = [(a +n– 1)(a+n – 2)..-a]3".

A: It is given in the question that X~Gammaα,β then we have to prove that for any positive integer n≥1.…

Q: Let tn be the n-th triangular number, starting with t1 = 1, t2 = 3, t3 = 6, %3D %3D etc. (a) Prove…

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Q: Suppose X~N(180,15), and Z~N(0,1). Then x = 185, is equivalent to z = ______. (Round your answer to…

A: Given that, x~N(180,15)  Mean = 180  standard deviation = 15  We know that z-score is given by,…

Q: 2. Consider the Newton polynomial Pn(z)= ao+a1 (1-10) + a₂(1-10) (1-11)+... +an(1-10)(1-1₁).…

A: Given that   that interpolate then we have Now  ,       putting

Q: Prove that : Σ j=1 m=1 2.

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Q: Prove = cos for some x in (0, π/2).

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Q: Verify that the sequence Un(x) = cos ( (n + n ɛ N form an orthogonal set of functions on [0,1]. That…

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Q: #25b, #25c

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Q: Determine discrete numeric function corresponding to the following generating function: A(Z)=1/1-Z³

A: Given generating function is A(z)=11-z3 We can write it as A(z)=1-z3-1⇒A(z)=1+z3+z6+z9+....

Q: Let f be a C1 function on [-7, 7]. Prove that the Fourier coefficients of f satisfy | an |< K | bn…

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Q: Let f (x), −L < x < L, be an odd function that satisfies the symmetry condition f (L −x) = −f (x)…

A: Given: Let us consider the given function fx, -L&lt;x&lt;L and the condition fL-x=-fx. To find: An=0…

Q: Find the number of pairs (m, n) of positive integers with 1 < m <n< 30 such that there exists a real…

A: Hope this will help you

Q: (a) Define F: z - Z by the rule F(n) = 2 - 3n, for each integer n. (i) Is F one-to-one? Suppose n,…

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Q: Suppose X~N(165,16), and Z~N(0,1). Then x = 173, is equivalent to z = ______. (Round your answer to…

A: Given: X~N(165,16) μ=165σ2=16Thus, σ=σ2=16=4 And X=173

Q: Find the absolute maximum and the absolute minimum of U(q) 20002 (15 5q)4 on the nterval 04.

A: First find the derivative of the given function and compute the critical points.

Q: 4) Let n-1 f(T) = T" +) a; · Ti i=0 be a monic polynomial of degree n > 1 with a; E Z for all 0 < i…

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