Problem 2 Let x equal a real number that is selected randomly from the closed interval from zero to ten. Use your intuition to assign values to
Problem 2 Let x equal a real number that is selected randomly from the closed interval...
2 Let x equal a real number that is selected randomly from the closed interval from zero to ten. Use your intuition to assign values to P{x: 0≤x≤3}=____________ P{x: x=3}=________________ P{x: 0≤x≤10}=_____________ P{x: x≥7}=_______________
Let X = the headway between two randomly selected consecutive cars (sec). Suppose that in a different traffic environment =, the distribution of time headway has the form: f(x) = {k/(x^5) if x >= 1, 0 if x <= 1 A: Determine the value of k for which f(x) is a legitimate pdf. B: Obtain the cumulative distribution function. C: Use the cdf form (b) to determine the probability that headway exceeds 2 sec and also the probability that headway...
(5) 2. Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose that the distribution of X is as follows: T 1 2 3 p(x) 3 .2 .5 A a random sample of size n-3 is selected. a) find pmf of Xn and construct a histogram, b) give two smallest values of S2, (S2 is the sample variance) and find their probabilities. (5) 2. Let X be the number of...
A spinner from a board game randomly indicates a real number between 0 and 20. The spinner is fair in the sense that it indicates a number in a given interval with the same probability as it indicates a number in any other interval of the same length. (a) Explain why the functionf(x) = f(x)= 0.05 if 0 ≤ x ≤ 20 0 if x < 0 or x > 20 is a probability density function for the spinner's values?...
Question 9 Let X and Y be the number of hours that a randomly selected person watches movies and sporting events, respectively, during a three-month period. The following information is known about X and Y: E(X) = 50 E(Y) = 20 Var(X) = 50 Var(Y) = 30 Cov(X,Y) = 10 One hundred people are randomly selected and observed for these three months. Let T be the total number of hours that these one hundred people watch movies or sporting events...
Let the random variable X count the number of adults out of five randomly selected adults who reported sleepwalking. The table gives the probability distribution of X X P(X=x) 0 0.142 1 0.353 2 3 0.137 4 0.042 5 0.006 A) Determine the missing probability that ensures the tables is a valid discrete probability distribution B) Compute the probability that among five randomly selected adults fewer than three report sleepwalking C) Compute the probability that among five randomly selected adults...
A real number is to be selected at random from the interval [-5, 5]. There is a probability of 0.7 that the result will fall in the range [-5, -1], and all numbers from that interval have the same relative likelihood. Each number in the range (-1, 3) has twice the relative likelihood as each number in the range [3, 5]. a. Plot the PDF and CDF of the random variable described by this probability distribution. b. Find the probability...
1) Let X and Y be random variables. Show that Cov( X + Y, X-Y) Var(X)--Var(Y) without appealing to the general formulas for the covariance of the linear combinations of sets of random variables; use the basic identity Cov(Z1,22)-E[Z1Z2]- E[Z1 E[Z2, valid for any two random variables, and the properties of the expected value 2) Let X be the normal random variable with zero mean and standard deviation Let ?(t) be the distribution function of the standard normal random variable....
(5 points) Let X be a Unif(-4, 4) variable, that is, X is Uniformly distributed over the interval (-4,4) Provide answers to the following to two decimal places Part a) Find the MGF of X, evaluated at the point = 1.52. 35.9397 Part b) Let Xi,X2,... , X, be independent Unif(-4,4) variables. Let Find the MGF My(t) of Y. Evaluate the MGF at the point t 0.38 in the case n 5 6.02326 Part c) Find the standard deviation of...
Let X denote the amount of time for which a book on 2-hour reserve at a college library is checked out by a randomly selected student and suppose that Xhas cumulative distribution function, CDF 4 1 2 2 Use this to compute the following a. P(Xs 1) b. P(0.5 XS1.5) d. Determine the median checkout duration. That is find x such that F(x) = 0.5. e. Compute F') to obtain the density function fo) f. Determine E(X) and Var(X). Let...