There are two varieties of cucumbers - C1 and C2 which have different distributions of length. The joint probability density function of the length of the cucumber and category 1 is denoted by p(x, C1), and is a uniform distribution over the range (10cm, 30cm). Similarly p(x, C2) is a uniform distribution over the range (20cm, 50cm). What is the error of classification we will make if we assert that all cucumbers of length less than 25cm are of Variety C1 and all cucumbers of length greater than 25cm are of Variety C2?.

There are two varieties of cucumbers - C1 and C2 which have different distributions of length. The joint probability density function of the length of the cucumber and category 1 is denoted by p(x, C1), and is a uniform distribution over the range (10cm, 30cm). Similarly p(x, C2) is a uniform distribution over the range (20cm, 50cm). What is the error of classification we will make if we assert that all cucumbers of length less than 25cm are of Variety C1 and all cucumbers of length greater than 25cm are of Variety C2?.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

a. Explain the difference between the method of moment generating function and the method of incarnation to find the probability density function of a random variable b. Let X1, X2, X3 ,,,,, each of them has Poisson distribution with parameter lamda 1, lamda2, lamda3,........ i. Get the probability distribution of Y=X1+X2+....Xn ii. Get the mean and variance of Y c. Y1 and Y2 be a joint probability function as shown below in the screenshot imageU=Y1/(Y1+Y2), Using the method of incarnation (Jacobian), find the probability density function of U
c) Let S and T be two independent random variables with probability density functions 1 f(s)= - s > 0, e elsewhere. (e) = t > 0, e 0. elsewhere. Given X = S+ Y and Y = T. Find a joint probability distribution function of X and Y. Then determine the marginal density function of Y.
Please answer i,i,ii, and show steps if possible. Do not randomly write wrong answers if don't know how to solve.
Suppose that we have an independent and identically distributed sample from some distribution family G defined by an unknown parameter value 0. The frequentist approach to statistics would treat e as a fixed value (constant), but the Bayesian approach to statistics would treat 0 as a random variable with some prior distribution specified by a probability density function 1(0). True O False
SECTION A: THEORY. 1. A) The amount of time it takes students to complete a Statistics II quiz is uniformly distributed between 30 to 60 minutes. One student is selected at random. Find the following: a. The probability density function (pdf) of amount of time taken for the quiz. b. The probability that the student requires more than 50 minutes to complete the quiz. c. The probability that the student completes the quiz in a time between 35 and 40 minutes. d. The probability that the student requires at least 45 minutes to complete the quiz. e. The probability that the student completes the quiz exactly 52 minutes. f. Compute the expected time and the coefficient of variation to complete the quiz. B) Using 95% confidence, how large a sample should be taken to obtain a margin of error for the estimation of a population proportion of 0.065? Assume that the data are not available for developing the planning value for n.
Suppose an industry produced a particular type of metal mixture up to 1 ton a day. Due to technical difficulties or system breakdowns, the actual amount produced by the industry is Y, a random variable which has the following Probability density function: f(y) = √2y 0
Two high school seniors find themselves with much time and nothing to do. They decide to devise a computer game in which a cursor moves randomly along the x axis between -2 and 2. The game they play is to stop the cursor at random points between -2 and 2 without looking at the screen. Such a game results in a uniform distribution overthe interval between -2 and 2 and resemebles a density curve. The height of the density curve is:
1. A continuous random variable X is defined by (3+x) f(x) - 3sxs-1 %3D 16 (6-2r) -1sxs1 16 (3-x) -1sxs3 16 a. Verify that f(x) is density. Explain b. Find the mean 2. If the probability density function of random variable is given by f(x) = wch 1srs2 sech x a. Find the mean b. Find the total area 3. If the probability density function of random variable is given by f(x) = sinh 2x 1sxs2 a. Find the mean b. Find the total area c. Illustrate the graph (use bell shaped figure) II II
If X and Y are independent RVs, each following N (0, 3), what is the probability that the point (X, Y) lies between the lines 3X + 4Y = 5 and 3X + 4Y = 10?
5. Suppose that X is a discrete random variable with probability density function p(x) = cx², x = 1, 2, 3, 4. (c) Find Var(X). Select one: O a. 18.4 O b. 354 O c. none O d. 342.8
1. Each rear tire on an experimental airplane is supposed to be lled to a pressure of 40 pounds per square inch (psi). Let Y1 denote the actual air pressure for the right tire and Y2 denote the actual air pressure for the left tire. Suppose that Y1 and Y2 are random variables with the joint density function attached as a photo. a) Find k. b) Find the joint distribution function for Y1 and Y2. c) Find the probability that both tires are underfilled.
1. The loss due to a fire in a commercial building is modelled by a random variable X with density function Let X be a random variable with probability distribution table given below 10 20 50 100 P(X=x) | 0.4 | 0.3 | 0.15 | 0.1 | 0.05 Prepare the cdf of X.