JuanPro
This page lists questions and answers that were posted by visitors named JuanPro.
Questions
The following questions were asked by visitors named JuanPro.
In this problem, you are given descriptions in words of certain events (e.g., "at least one of the events A,B,C occurs"). For each one of these descriptions, identify the correct symbolic description in terms of A,B,C from Events E1-E7 below. Also identif...
11 years ago
PROBLEM 2: SET OPERATIONS AND PROBABILITIES (3 points possible) Find the value of P(A∪(Bc∪Cc)c) for each of the following cases: The events A, B, C are disjoint events and P(A)=2/5. P(A∪(Bc∪Cc)c)= incorrect The events A and C are disjoint, and P(A)=1/2 an...
11 years ago
PROBLEM 4: PARKING LOT PROBLEM (3 points possible) Mary and Tom park their cars in an empty parking lot with n≥2 consecutive parking spaces (i.e, n spaces in a row, where only one car fits in each space). Mary and Tom pick parking spaces at random. (All p...
11 years ago
Alice and Bob each choose at random a real number between zero and one. We assume that the pair of numbers is chosen according to the uniform probability law on the unit square, so that the probability of an event is equal to its area. We define the follo...
11 years ago
A boat leaves point P on one side of a river bank and travels with constant velocity V in a direction towars point Q on the other side of the river directly oposite P and distance D from it If r is the instantaneous distance from Q to the boat, θ is the a...
11 years ago
Let X and Y be normal random variables with means 0 and 2, respectively, and variances 1 and 9, respectively. Find the following, using the standard normal table. Express your answers to an accuracy of 4 decimal places. 1 P(X>0.75)= 2 P(X≤−1.25)= 3 Let Z=...
11 years ago
Random variables X and Y are distributed according to the joint PDF fX,Y(x,y) = {ax,0,if 1≤x≤2 and 0≤y≤x,otherwise. 1 Find the constant a. a= 2 Determine the marginal PDF fY(y). (Your answer can be either numerical or algebraic functions of y). For 0≤y≤1,...
11 years ago
t the discrete random variable X be uniform on {0,1,2} and let the discrete random variable Y be uniform on {3,4}. Assume that X and Y are independent. Find the PMF of X+Y using convolution. Determine the values of the constants a, b, c, and d that appear...
11 years ago
Consider n independent rolls of a k-sided fair die with k≥2: the sides of the die are labelled 1,2,…,k and each side has probability 1/k of facing up after a roll. Let the random variable Xi denote the number of rolls that result in side i facing up. Thus...
11 years ago
Consider the random variables X, Y and Z, which are given to be pairwise uncorrelated (i.e., X and Y are uncorrelated, X and Z are uncorrelated, and Y and Z are uncorrelated). Suppose that E[X]=E[Y]=E[Z]=0, E[X2]=E[Y2]=E[Z2]=1, E[X3]=E[Y3]=E[Z3]=0, E[X4]=...
11 years ago
A fair coin is flipped independently until the first Heads is observed. Let K be the number of Tails observed before the first Heads (note that K is a random variable). For k=0,1,2,…,K, let Xk be a continuous random variable that is uniform over the inter...
11 years ago
Fred is giving away samples of dog food. He makes visits door to door, but he gives a sample away (one can of dog food) only on those visits for which the door is answered and a dog is in residence. On any visit, the probability of the door being answered...
11 years ago
Suppose that you have two laptops, both of which you begin using at time 0. Each laptop will eventually fail, and we model each one's lifetime as exponentially distributed with the same parameter λ. The lifetimes of the two laptops are independent. One of...
11 years ago
In parts 1, 3, 4, and 5 below, your answers will be algebraic expressions. Enter 'lambda' for λ and 'mu' for μ. Follow standard notation. Shuttles bound for Boston depart from New York every hour on the hour (e.g., at exactly one o'clock, two o'clock, etc...
11 years ago
Consider a Poisson process with rate λ. Let N be the number of arrivals in (0,t] and M be the number of arrivals in (0,t+s], where t>0,s≥0. In each part below, your answers will be algebraic expressions in terms of λ,t,s,m and/or n. Enter 'lambda' for λ a...
11 years ago
PROBLEM 7: SAMPLING FAMILIES (3 points possible) We are given the following statistics about the number of children in the families of a small village. There are 100 families: 10 families have no children, 40 families have 1 child each, 30 families have 2...
11 years ago
Problem 4: Variational principle and bounds (3 parts, 30 points) PART A (15 points possible) Consider a particle of mass m in a box of size L so the wave function vanishes at x=±L/2. Find an upper bound E∗ on the ground state energy Egs using a simple tri...
10 years ago
A rectangular wire loop with current i=200mA, width W=20cm and length L=50cm is placed in a uniform magnetic field B=7T as shown. The normal to the loop, represented by the dashed line, is θ=20degrees from the magnetic field direction. #3A (6 points possi...
10 years ago
#6 (6 points possible) The demonstration in LS6.U5 uses a Helmholtz coil, which is a pair of wire coils along a common axis that creates a somewhat uniform magnetic field at the center. To achieve a uniform field, the coil separation is equal to the coil...
10 years ago
Two identical bar magnets A and B are held at rest as shown and released to fall simultaneously. Magnet A as it falls passes through the center of a copper ring, magnet B does not. #9 (4 points possible) Which of the following statements is true? - unansw...
10 years ago
A series RLC circuit is made with a C=100pF capacitor, an L=100μH inductor, and an R=30Ω resistor. The circuit is driven at 5×106rad/s with a 1V amplitude. #12A (4 points possible) What is the current oscillation amplitude in A? What is the current oscill...
10 years ago
F.(0) (10 puntos posibles) C1 What is limh→0cos(π6+h)−cos(π6)h? (Enter the answer as a decimal. If the limit does not exist, enter DNE.) sin responder Loading C2 At which of the five points on the graph are dydx and d2ydx2 both negative? Click all that ap...
10 years ago
Find the tangent line to the curve xy3+2y−2x=1 through the point (x,y)=(1,1). (Enter ∗ for multiplication: type 2*x for 2x. Enter / for division: type 1/2 for 12.) Tangent Line y=
10 years ago
A person is jumping straight up and down on a trampoline. The height of the center of mass of the person is measured every tenth of a second. It takes just over one second to complete one full bounce. (If you want to see the data, look at the video above....
10 years ago
Answers
The following answers were posted by visitors named JuanPro.