Homework Answers
Add Answer to:
1. (a) A point is selected at random on the unit interval, dividing it into two pieces with total length 1. Find the probability that the ratio of the length of the shorter piece to the length of the...
1. (a) A point is selected at random on the unit interval, dividing it into two pieces with total length 1. Find the pr...
1. (a) A point is selected at random on the unit interval, dividing it into two pieces with total length 1. Find the probability that the ratio of the length of the shorter piece to the length of the longer piece is less than 1/4 3 marks (b) Suppose X, and X2 are two iid normal N(μ, σ2) variables. Define Are random variables V and W independent? Mathematically justify your answer. 3 marks] (c) Let C denote the unit circle...
Suppose that a point is chosen at random on a stick of unit length and that the stick is broken into two pieces at that point. Then, we form a right angle with two pieces of stick, forming the two sho...
Suppose that a point is chosen at random on a stick of unit length and that the stick is broken into two pieces at that point. Then, we form a right angle with two pieces of stick, forming the two shorter sides of a right-angled triangle. Let Θ be the smallest angle in this triangle. Define Y = tanΘ and W = cotΘ. Find E(Y ) and the p.d.f of W.
A piece of lumber of fixed length L is broken into two sub-pieces at position X...
A piece of lumber of fixed length L is broken into two sub-pieces at position X ~ U(0, L). Let Y denote the length of the shorter sub-piece. a) Find the cumulative distribution function of Y. Hint: First express Y as a piecewise function in terms of X. b) Find the probability distribution function of Y. Identify the name of the distribution that Y follows. Also, write down the parameter value(s) of this distribution.
(1 point) Two points are selected randomly on a line of length 16 so as to...
(1 point) Two points are selected randomly on a line of length 16 so as to be on opposite sides of the midpoint of the line. In other words, the two points X and Y are independent random variables such that X is uniformly distriuted over [0,8) and Y is uniformly distributed over (8,16] Find the probability that the distance between the two points is greater than 6. P(|X – Y| > 6) =
(1 point) Two points are selected randomly on a line of length 10 so as to...
(1 point) Two points are selected randomly on a line of length 10 so as to be on opposite sides of the midpoint of the line. In other words, the two points X and Y are independent random variables such that X is uniformly distributed over [0,5) and Y is uniformly distributed over (5, 10]. Find the probability that the distance between the two points is greater than 2. answer:
)on 4. Suppose X and y are continuous random variables with joint density funstion the unit...
)on 4. Suppose X and y are continuous random variables with joint density funstion the unit square [0, 1] x [0, 1]. (a) Let F(r,y) be the joint CDF. Compute F(1/2, 1/2). Compute F(z,y). (b) Compute the marginal densities for X and Y (c) Are X and Y independent? (d) Compute E(X), E(Y), Cov(X,y)
Exercise about two-dimensional random variables, independence and covariation: Suppose, two-dimensional random variable...
Exercise about two-dimensional random variables, independence
and covariation:
Suppose, two-dimensional random variable (X, Y) has probability density function as follows: 0y1 + f(x, y) 2xy) ,0 <x<1, otherwise 0 Find c Find marginal probability density functions of X and Y-find f(x) and f(y) and find if X and Y are independent; Find joint (X, Y) distribution function; Find covariation of X and Y find Cov(X, Y) and correlation p(X, Y). What can be concluded?
Suppose, two-dimensional random variable (X, Y)...
4. A random point (X, Y ) is chosen uniformly from within the unit disk in R2, {(x, y)|x2+y2< 1} (a) Let (R, O) deno...
4. A random point (X, Y ) is chosen uniformly from within the unit disk in R2, {(x, y)|x2+y2< 1} (a) Let (R, O) denote the polar coordinates of the point (X,Y). Find the joint p.d.f. of R and . Compute the covariance between R and 0. Are R and e are independent? (b) Find E(XI{Y > 0}) and E(Y|{Y > 0}) (c) Compute the covariance between X and Y, Cov(X,Y). Are X and Y are independent?
4. A random...
f(x,y)=0 2. (20 marks) Suppose X and Y are jointly continuous random variables with probability density...
f(x,y)=0 2. (20 marks) Suppose X and Y are jointly continuous random variables with probability density function fc, 0<x<1, 0<y<1, x + y>1 else a) (2.5 marks) Find the constant, c, so that this is valid joint density function. b) (5 marks) Find P(Y > 2X). c) (5 marks) Find P(X>0.5 Y = 0.75). d) (5 marks) Find P(X>0.5 Y <0.75). e) (2.5 marks) Are X and Y independent? Justify your answer citing an appropriate theorem.
suppose that two random variables X and Y have joint Pdf, f(x,y) = 1/√2π * e^(-((x2y2)/2)-y)...
suppose that two random variables X and Y have joint Pdf, f(x,y) = 1/√2π * e^(-((x2y2)/2)-y) * y2 -inf < x < inf and y > 0 a) Are X and Y independent? Justify. b) Find the distribution of Y
1. (a) A point is selected at random on the unit interval, dividing it into two pieces with total length 1. Find the probability that the ratio of the length of the shorter piece to the length of the longer piece is less than 1/4 3 marks (b) Suppose X, and X2 are two iid normal N(μ, σ2) variables. Define Are random variables V and W independent? Mathematically justify your answer. 3 marks] (c) Let C denote the unit circle...
(1 point) Two points are selected randomly on a line of length 16 so as to be on opposite sides of the midpoint of the line. In other words, the two points X and Y are independent random variables such that X is uniformly distriuted over [0,8) and Y is uniformly distributed over (8,16] Find the probability that the distance between the two points is greater than 6. P(|X – Y| > 6) =
(1 point) Two points are selected randomly on a line of length 10 so as to be on opposite sides of the midpoint of the line. In other words, the two points X and Y are independent random variables such that X is uniformly distributed over [0,5) and Y is uniformly distributed over (5, 10]. Find the probability that the distance between the two points is greater than 2. answer:
)on 4. Suppose X and y are continuous random variables with joint density funstion the unit square [0, 1] x [0, 1]. (a) Let F(r,y) be the joint CDF. Compute F(1/2, 1/2). Compute F(z,y). (b) Compute the marginal densities for X and Y (c) Are X and Y independent? (d) Compute E(X), E(Y), Cov(X,y)
Exercise about two-dimensional random variables, independence
and covariation:
Suppose, two-dimensional random variable (X, Y) has probability density function as follows: 0y1 + f(x, y) 2xy) ,0 <x<1, otherwise 0 Find c Find marginal probability density functions of X and Y-find f(x) and f(y) and find if X and Y are independent; Find joint (X, Y) distribution function; Find covariation of X and Y find Cov(X, Y) and correlation p(X, Y). What can be concluded?
Suppose, two-dimensional random variable (X, Y)...
4. A random point (X, Y ) is chosen uniformly from within the unit disk in R2, {(x, y)|x2+y2< 1} (a) Let (R, O) denote the polar coordinates of the point (X,Y). Find the joint p.d.f. of R and . Compute the covariance between R and 0. Are R and e are independent? (b) Find E(XI{Y > 0}) and E(Y|{Y > 0}) (c) Compute the covariance between X and Y, Cov(X,Y). Are X and Y are independent?
4. A random...
f(x,y)=0 2. (20 marks) Suppose X and Y are jointly continuous random variables with probability density function fc, 0<x<1, 0<y<1, x + y>1 else a) (2.5 marks) Find the constant, c, so that this is valid joint density function. b) (5 marks) Find P(Y > 2X). c) (5 marks) Find P(X>0.5 Y = 0.75). d) (5 marks) Find P(X>0.5 Y <0.75). e) (2.5 marks) Are X and Y independent? Justify your answer citing an appropriate theorem.
Most questions answered within 3 hours.
-
An entomologist discovers a dung beetle rolling a ball of dung
along the ground, and decides...
asked 58 minutes ago -
Humans have used horses for transportation for millions of
years. Therefore, they will use horses for...
asked 2 hours ago -
The following are the Jensen Corporation's unit costs of making
and selling an item at a...
asked 3 hours ago -
Does direct Medicare reimbursement of Advanced practice nurses
increase access to their services?
asked 4 hours ago -
List and explain why a company would choose to use a
published
compensation survey vs. creating...
asked 4 hours ago -
A discrete random variable X can take values from 1 to 10. Find
the variance of...
asked 4 hours ago -
The primary financial goal of a corporation is to maximize:
shareholders wealth.
earnings per share.
stock...
asked 4 hours ago -
determine whether the vectors u=(1,2,3,), v=(-2,1,0) and
w=(1,0,1) are linearly dependent or independent.
asked 4 hours ago -
python
Define a function called print_values which takes a dictionary
object as a parameter. The function...
asked 5 hours ago -
In Chapter 1 you created a program named Triangle in
which you displayed a seven-line triangle...
asked 5 hours ago -
Research question: What are the differences between separately
stated and non separately stated transactions in an...
asked 6 hours ago -
By using Arduino write a code that connects two LEDs to two
push-buttons. Each button controls...
asked 7 hours ago