Question

In: Math

Problem 6. 1. If X N(9; 4), nd Pr(jX ? 2j < 4). 2. If X...

Problem 6.
1. If X N(9; 4), nd Pr(jX ? 2j < 4).
2. If X N(0; 1), nd Pr(jX + 3j > 5).
3. If X N(?2; 9), nd the number c such that Pr(jX + 2j < c) = 0:5.

Expert Solution

1] If X N(9; 4), find

=

= 0.06680720 - 0.000000000189

= 0.06680718

2. If X N(0; 1), find

= 1 - [ 0.977250 - 0.000000006 ]

= 0.02275

3. If X N(-2; 9), find the number c such that = 0.5

= 0.5

Where Z is Standard normal variate

= 0.5

= 0.75

c/3 = 0.67449

c = 2.023469

milcah answered 6 months ago

8. Suppose X~N(100,15), what is Pr(100<X<130) 9. Suppose X~N(100,15), what is Pr(100<X<130) 10. Suppose X~N(100,15), what...

8. Suppose X~N(100,15), what is Pr(100<X<130) 9. Suppose X~N(100,15), what is Pr(100<X<130) 10. Suppose X~N(100,15), what is Pr(X<120) 11. Suppose X~N(100,15), what is Pr(85<X<130) 12. Suppose X~N(150,25), what is Pr(140<X<165)

Show by induction that for all n natural numbers 0+1+4+9+16+...+ n^2 = n(n+1)(2n+1)/6.

1: Given that f(4) = 6 and f'(x) = 2/x2+9 for all x. a) Use a...

1: Given that f(4) = 6 and f'(x) = 2/x2+9 for all x. a) Use a linear approximation or differentials to estimate f(4.04) b) Is your estimate in part (a) too large or too small? Explain. 2: a) Given f(x) = (x + 3)sinx, find f'(π) using logarithmic differentiation. b) Find the value of h'(0) if h(x)+xsin(h(x))= x2+4x-π/2

Solve the given initial-value problem. X' = 2 4 −1 6 X, X(0) = −1 8...

Solve the given initial-value problem. X' = 2 4 −1 6 X, X(0) = −1 8 X(t) =

1. compute the least non-negative residue of 4^n (mod 9) for n=1,2,3,4,5.... prove that 6*(4^n)=6 (mod...

1. compute the least non-negative residue of 4^n (mod 9) for n=1,2,3,4,5.... prove that 6*(4^n)=6 (mod 9) for every n>0. 2. find nice tests for divisibility of numbers in base 34 by each of 2,3,5,7,11,and 17. 3. in Z/15Z, find all solutions of : (i) [36]X=[78]. (ii) [42]X=[57] (iii) [25]X=[36] 4. in Z/26Z, find the inverse of [9], [11], [17], and [22] 4. write the set of solutions of x=5 mod24. x=17 (mod 18) for all equation line, there are...

A=[ 7 8 -2 -6 7 4 1 ; 2 4 -4 -13 9 9 -12...

A=[ 7 8 -2 -6 7 4 1 ; 2 4 -4 -13 9 9 -12 ; 6 6 0 -9 8 9 -4 ; 1 8 -14 -22 5 8 -1 ; 4 9 -10 -14 7 4 -1] B=[ 19 4 4 14 -3 -7 -5 ; 21 -6 -5 10 14 -2 4 ; 22 -4 5 13 5 -6 4 ; 41 20 0 26 11 -1 -27 ; 29 14 -2 20 3 -4 -19]...

Algorithm problem 4 [3.1-4] Is (2^(n+1))∈O(2^n)? Is (2^(2n))∈O(2^n)?

Table: x: 6, 2, 15, 9, 12, 5, 8 y: 8, 9, 4, 7, 6, 9,...

Table: x: 6, 2, 15, 9, 12, 5, 8 y: 8, 9, 4, 7, 6, 9, 8 1) Make the scatter diagram. 2) Find the equation of the regression line using the formulas given in class. They must appear the intermediate steps of substitutions. Round the answers to three decimal places. 3) Find the correlation coefficient using the formulas given in class. Steps should appear intermediates of substitutions. Round the answer to three decimal places. 4) Find the value predicted...

#2 The Jacobsthal sequence is defined by J(1)=J(2)=1 and J(n)=J(n-1)+2J(n-2). Use recursion to write a function...

#2 The Jacobsthal sequence is defined by J(1)=J(2)=1 and J(n)=J(n-1)+2J(n-2). Use recursion to write a function that takes in a positive integer n and returns the nth Jacobsthal number. >>> J(8) 85 >>> J(9) 171 #3 Use recursion to write a function that takes in a positive integer n and returns all n digit numbers containing only odd digits. >>> f(1) [1, 3, 5, 7, 9] >>> f(2) [11, 13, 15, 17, 19, 31, 33, 35, 37, 39, 51, 53,...

Prove the following by induction: 2 + 4 + 6 + …+ 2n = n(n+1) for...

Prove the following by induction: 2 + 4 + 6 + …+ 2n = n(n+1) for all integers n Show all work