Assume that x is a uniformly distributed random number between 0 and 1 (e.g. x is the RAND() function in Excel), and that the number of units to be sold is uniformly distributed between 100 and 400. In this case, sales are given by the expression:
400 - 100 * x
100 + 400 * x
400 + x
300 + / - x
Assume that x is a uniformly distributed random number between 0 and 1 (e.g. x is...
5000) of uniformly distributed random numbers between 1 Generate a large number (1000 or and 2 (HINT: use the rand command for generating a uniformly distributed random variable between 0 and 1 and then move it!). b Plot the pdf of the distribution. Use the hist command to obtain the number of samples in a random numbers, define binx as a vector with bins on the x-axis (binx = 1:0.01:2). P histx,binx) will provide you the weights pdf. Compare with...
Problem 2. Suppose that a uniformly distributed random number X in [0, 1] is found by calling a random number generator. Then, if the call to the RNG produces the value r for X, another random number Y is computed that is uniformly distributed on (0, x). That is, X is uniform on the interval [0, 1], and the conditional distribution for Y given X -a is uniform on the interval [0,x] a) Calculate E(Y X-0.4). b) Calculate E (X...
Problem 5. Suppose that a uniformly distributed random number X in 0 is found by calling a random number generator. Then, if the call to the RNG pro- duces the value r for X, another random umber Y is computed that is uniformly distributed on 0, . That is, X is uniform on the interval 0,1], and the conditional distribution for Y given X = 1 is uniform on the interval [0.11 a) Give fonmulas for E(Y X) and Var(Y...
Many random number generators allow users to specify the range of the random numbers to be produced. Suppose that you specify that the range is to be all numbers between 0 and 5. Call the random number generated Y. Then the density curve of the random variable Y has constant height between 0 and 5, and height 0 elsewhere. 1. Use Excel to generate 100 random values from the above distribution. Construct a histogram for generated values [ Note: use...
The random variable X is known to be uniformly distributed between 2 and 12. Compute E(X), the expected value of the distribution. Please explain how to do this using EXCEL.
Assume random variable ? is uniformly distributed in the interval (−?/2 ,?⁄ 2]. Define the random variable ?=tan (?), where tan (∙) denotes the tangent function. Note that the derivative of tan (?) is 1/(cos (?)2) . a) Find the PDF of ?. b) Find the mean of ? .Define the random variable ?=1/?. c) Find the PDF of ?. Assume random variable X is uniformly distributed in the interval (-1/2, 1/2). Define the random variable Y = tan(X), where...
1#x is a number chosen uniformly at random between 0 and 1, what is the probability that the greatest integer s logal is odd? 4-6 4-6.
Let X be a uniformly distributed continuous random variable that lies between 1 and 10. i. Sketch the probability density function for X. ii. Find the formula for the cumulative distribution for X and use it to compute the probability that X is less than 6
Let X be a uniformly distributed random variable on [0,1]. Then, X divides [0,1] into the subintervals [0,X] and [x,1]. By symmetry, each subinterval has a mean length 0.5. Now pick one of the subintervals at random in the following way: Let Y be independent of X and uniformly distributed on [0,1], and pick the subinterval [0,X], or (X,1] that Y falls in. Let L be the length of the subinterval so chosen. What is the mean length of L...
Instructions: If you require uniformly distributed random numbers in [0, 1], use Matlab’s built in uniform random number generator rand. Also, you may NOT use any Matlab built-in functions that explicitly perform the task asked for in the problem. Problem 6. Let α > 0 and set f(x)- ae-ale, for x e(-oo, oo). (a) Make a plot of f (b) Show that f is a probability density function (Hint: -, when z S 0, and x-r, when 0.) (c) If...