2.38. Find: (a) 10!, 11!, 12! (b) 60! (Hint: Use Stirling's approximation to n!.)

Q: Find 3 values of r n =120 o(n) such that

A: Ok

Q: (c) P(\X| > 3) (d) P(|X – 5| > 3)

A: We have given that.   X~N( μ , ?^2 )   μ=5 , ? =1   Z-score =( x - μ )/?

Q: 5. (a) If r23 = 0, prove that R₁ (23) = (23) = 712 + 7³1 01-23 = (1 - 12 - 13). 07.

A:

Q: The total voting-age population P (in millions) in the United States from 1990 through 2014 can be…

A:

Q: 5s L |(s – 2)

A:

Q: Find f(t) for each of the following functions: 18s + 66s + 54 a) F(s) (s + 1)(s + 2)(s + 3)' 8s +…

A: The Laplace transform of a function ft is denoted by the function Lft=Fs. The Laplace transform is…

Q: 6. Show that, for integer s, S. s! | x25+lexp(-ax²)dx =: 2a +1

A: Note: Given proof statement has a little mistake, I have proof the actual result. First i have…

Q: If g(t) = £? (e-35-*), a farmula for L (e* g14) is? -8t +8 a) ede+25 b) e 3e+17

A: Given g(t)=ℒ-1e-3s-7

Q: 2.24 Derive the simplest sum-of-products expression for the function f(x₁, x2, x3, x4) X₁ X3 X4 +…

A: we have to derive the simplest sum-of-products expression for the functionFor the given function,…

Q: Let F (z, y, z)=47'yzi+10zj-2zyk and a smooth curve C given by the line segment from (-1,2,0) to (2,…

A:

Q: 5- Find L-1 5² (s²+4)² by using Convolution theorem.

A:

Q: Q2. Consider Xi 0.12 yi 0.7917 0.7733 0.7437 0.24 0.36 0.48 0.7041 0.6563 0.6023 0.60 0.72 Using…

A:

Q: If I (F14)- s²+1 SO is given by? a) V(s? + 1)³

A:

Q: 9. Find a calculus-based approximation for V10 – (.92)² –- 2(2.03)².

A:

Q: 8. Determine (MN)-1 where M (:) 5 and N -5 2

A: The given matrices are M=8541  and  N=5-1-52. Evaluate MN as follows.…

Q: (1.2) Show that m m+n+1] m k=0 for any two positive integers m and n.

A: Please check the next step for detailed answer.

Q: 1. D, [3x²y+In(xy²)] За + In(xg In(xy³)]

A: Given,

Q: Let n 2 2. Assume that Fn is prime. show that -1.

A:

Q: 17. Let P1.Pn be positive real numbers such that P1+ + Pn=1. (a) Prove the following: @P² ≥ (ii)…

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Q: Give a recursive definition with initial condition(s). a) The function f(n) = 5", n = 0, 1, 2, ....…

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Q: b) Evaluate UTM L{t*e- 6(t-2)}. TM

A:

Q: 3. For n e N, we define n! = (n)(n – 1)(n – 2)... (2)(1). E.g., 4! = (4)(3)(2)(1) = 24. Prove the…

A: Here we have to prove two statements.

Q: Theorem = 7 K 51 M 25

A:

Q: Find F(0) if F (t) == L-! 16 82 (s+4) O 16 O 4 O 2

A:

Q: (1 2 43) 32 1. IF A = THEN (A) (B) (X Y) Z W

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Q: Show that (an) is increasing

A:

Q: 3. Prove that 6|(9" - 3") for all n E Z+.

A:

Q: _. . Prove that z² = + Emo(-1)" (n + 1) (²2)", where |z-21 < 2.

A:

Q: I dont understand how we go from P(B) = P(A) + P(B ∩ A') to P(B) ≥ P(A)

A: A,B  belongs to F  We have to prove that If A ⊂B then  P(A)≤ P(B)

Q: 1. It has been shown that if m divides n, then Fm is a factor of Fn. Show that this is true for the…

A:

Q: (9x + 3) D. (5x-2)" (11r-21) Find m<D. (Not x but m<D)

A:

Q: a) f(t) = esec(20) + In(2t² + 5)

A:

Q: (d) If each fn has fewer than M discontinuities (where M ∈ N is fixed), thenf has fewer than M…

A: To Show: If each fn has fewer than M discontinuities (where M ∈ N is fixed), then f has fewer than M…

Q: 4(-1)" Σ 3) Estimate 2N 1 correct to one decimal place. N-1

A:

Q: A17 Let Xx² (99). What is Var(X)? Answer to A17:

A: X~chi square (99) We have to find var(X)