### Random-Number Generator and Uniform Probability DistributionThe random-number generator on calculators randomly generates a number between 0 and 1. The random variable $X$, the number generated, follows a uniform probability distribution.#### Tasks**(a)** Identify the graph of the uniform density function.**(b)** Calculate the probability of generating a number between 0.63 and 0.76.**(c)** Calculate the probability of generating a number greater than 0.83.#### Explanation of GraphsThere are three graphs labeled A, B, and C, showing potential uniform density functions:- **Graph A**: Displays a constant density of 1 for $x$ values between 0 and 1, and 0 elsewhere.- **Graph B**: Shows a density function with a constant value of 0.8, which is incorrect for a uniform distribution from 0 to 1.- **Graph C**: Displays a density function constant at 0.5, which is incorrect for the described distribution.**Selecting the Correct Graph:**For a uniform distribution between 0 and 1, the graph should have a constant density of 1 over this range, making **Graph A** the correct choice.#### Probability Calculations**(b)** Calculate the probability of generating a number between 0.63 and 0.76.- Probability = (0.76 - 0.63) = 0.13**(c)** Calculate the probability of generating a number greater than 0.83.- Probability = (1 - 0.83) = 0.17These calculations are based on the properties of a uniform distribution, where the probability is equivalent to the length of the interval within the given range [0, 1].

# random variable x follow uniform (0,1) 1): Then graph the density function 2): probability that number lies between 0.63 and 0.76 3): probability that number greater than 0.83

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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...

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