A random variable X has a distribution p(X=k) = A / (k(k+1)), k = 1,2,...,4, where A is an constant. Then compute the value of p(1<=X<=3)
The answer will be either: 2/3, 3/4, 5/6, or 15/16
A discrete random variable X is uniformly distributed among −1,0,...,12. Then, what is its PMF for k=−1,0,...,12
The answer will be either: p(X = k) = 1/12, 1/13, 1/14, or 1
In: Math
Theorem 1 (Mean Value Theorem). Suppose ? ⊂ R is open and ? : ? → R. If ? is differentiable on the open interval (?, ?) ∈ ? then there exists ? ∈ (?, ?) such that ?(?) − ?(?) ? − ? = ? ′ (?).
4. An alternative interpretation of the Mean Value Theorem is that if ? is differentiable on (?, ? + ℎ), then there exists ? ≤ ? ≤ ? + ℎ such that ?(? + ℎ) = ?(?) + ??(?)(ℎ) (1)
a. The Mean Value Theorem fails if ? : R^? → R^? even with ? = 1 and ? = 2. Let ? : [0, 1] → R^2 be given by ?(?) = (? − ?^2 , ? − ?^3 ). Show that Equation (1) fails for ? when ? = 0 and ℎ = 1.
b. On the other hand, let ?(?, ?, ?) = ?? + ?^2 , a = (0, 0, 0) and b = (2, 1, 2). Let ? : [0, 1] → R^3 be the parameterization of the line segment going from a to b. Find (? ∘ ?)(?) and (? ∘ ?) ′ (?).
c. Find a value ?0 ∈ (0, 1) such that ?(b) − ?(a) = (? ∘ ?) ′ (?0).
In: Advanced Math
X value:1, 1, 1, 3, 3, 3, 3, 5, 5, 5 (months)
Y value: 4.7, 3.1, 4.0, 14.8, 13.4, 15.6, 14.2, 23.5, 22.2, 24.4 (kg)
1. Find the value of the linear correlation coefficient, write down the formula
2. Find the equation of the least squares regression line y = b0 + b1x
3. If a 4-month old puppy comes , what do you expect its weight?
4. If you record 2-months old puppy's weight by its residual value of -0.84kg, Find the puppy's acutual weight
In: Statistics and Probability
Find the vertical and horizontal intercepts of each function.
7. f(t)= 2 (t-1) (t+2) (t-3)
12. C(t)= 4t^4+12t^3-40t^2
In: Math
In: Nursing
1) Define three types of environmental ethics and give example of each.
2) Write your opinion toward the: (2 marks each x 2 = 4 marks)
a) Increase the number of cars in the roads.
b) Increase the fishing process.
3) Prepare cost benefit draw for reducing waste from water emitted from industries?
4) Comment on your draw in question 3?
In: Economics
ONLY IN C LANGUAGE Write a C program to print all the unique elements of an array. Print all unique elements of an array Enter the number of elements to be stored in the array: 4 Input 4 elements in the arrangement: element [0]: 3 element [1]: 2 element [2]: 2 element [3]: 5 Expected output: The only items found in the array are: 3 5
In: Computer Science
Question: 3
There are four witnesses to a theft crime and investigator found
out that if the witness 1 is telling
truth so is the witness 2, the witness 2 and the witness 3 can’t
both be telling the truth, the
witness 3 and witness 4 are not both lying. And lastly if witness 4
is speaking truth then witness 2 is not
speaking truth. Tell us who are telling truth and who lies.
In: Computer Science
Find (a) the rank of the matrix below, (b) a basis for its row space, and (c) a basis for the solution space of Ax=0. [To save you time, I include the RREF of A.]
A = {(1,2,-3), (2, -1, 4), (4, 3, -2)}; each triple is a row of A, from left to right (top to bottom).
The RREF of A is {(1,0,1), (0,1,-2), (0,0,0)} (left to right, top to bottom, as above).
In: Advanced Math
In the face of the global financial crisis, Kevin Rudd introduced government guarantees on deposits.
Discuss covering at least the following two parts:
1. An introduction/summary of the Government Guarantee.
2. The general impact of this policy to the efficient frontier based on the Australian environment.
(1 paragraph on each part) (2 + 2 = 4 marks)
In: Economics