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real numbers that are uniformly distributed between 0 and 100. Find the probability that a random number (X) generated is between 10 and 90. Calculate the mean and variance of X.

real numbers that are uniformly distributed between 0 and 100. Find the probability that a random number (X) generated is between 10 and 90. Calculate the mean and variance of X.

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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5. Suppose that a random number generator produces real numbers that are uniformly distributed between 0 and 100. Suppose that a random number generator produces real numbers that are uniformly distributed between 0 and 100. Find the probability that a random number (X) generated is between 10 and 90. Calculate the mean and variance of X.
Transcribed Image Text:5. Suppose that a random number generator produces real numbers that are uniformly distributed between 0 and 100. Suppose that a random number generator produces real numbers that are uniformly distributed between 0 and 100. Find the probability that a random number (X) generated is between 10 and 90. Calculate the mean and variance of X.
•Types of functions to express probability distribution (a) Probability Mass Function (PMF) f(x) = P(x = x) (b) Cumulative Distribution Functions (CDF) f(x) = P(X ≤ x) Mean M = { xf(x) Variance 0² = [x²f (x) - μ² Standard Deviation. 0x Tot Discrete Uniform Distribution f(x) = //12 M = 0² = b+ a 2 (b-a+1)² 12 •Binomial Distribution (f(x) = (~) p² (1-P)^-x с пр np(1-P) 1• Hypergeometric Distribution (*) (*) (~) f(x) = и = пр 8² = np(1-P/(N=1) where K/N P= ·Poisson Distribution -^+ (^T)* X! f(x) = e M = AT 0² = NT Where N = population size sample size /no. of trials P probability - p = probability of success on a single trial K = no. of successes in the population in the sample of X - no. successes
Transcribed Image Text:•Types of functions to express probability distribution (a) Probability Mass Function (PMF) f(x) = P(x = x) (b) Cumulative Distribution Functions (CDF) f(x) = P(X ≤ x) Mean M = { xf(x) Variance 0² = [x²f (x) - μ² Standard Deviation. 0x Tot Discrete Uniform Distribution f(x) = //12 M = 0² = b+ a 2 (b-a+1)² 12 •Binomial Distribution (f(x) = (~) p² (1-P)^-x с пр np(1-P) 1• Hypergeometric Distribution (*) (*) (~) f(x) = и = пр 8² = np(1-P/(N=1) where K/N P= ·Poisson Distribution -^+ (^T)* X! f(x) = e M = AT 0² = NT Where N = population size sample size /no. of trials P probability - p = probability of success on a single trial K = no. of successes in the population in the sample of X - no. successes
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