The 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.(a) Identify the graph of the uniform density function.(b) What is the probability of generating a number between 0.2 and 0.72?(c) What is the probability of generating a number greater than 0.88?.....(a) Choose the correct graph of the uniform density function below.A.В.OC.Density1.2-Density1.2-1-0.8-0.6-0.4-0.2-0+Density1.2-1-1-0.8-0.6-0.4-0.2-0-0.8-0.6-0.4-0.2-0+0.2 0.4 0.6 0.811.20 0.2 0.4 0.6 0.811.20 0.2 0.4 0.6 0.811.2

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Answered: The random-number generator on…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The 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. (a) Identify the graph of the uniform density function. (b) What is the probability of generating a number between 0.48 and 0.62? (c) What is the probability of generating a number greater than 0.85? (a) Choose the correct graph of the uniform density function below. O A. O B. Density 1.2- 1- 0.8- 6. 0.6- 0 0.2 0.4 0.6 0.8 11.2 0.4- 0.2- to (b) The probability is (c) The probability is Q M (Simplify your answer.) (Simplify your answer.) ADensity 1.2- 1- 0.8- 0.6- 0.4- 0.2- to 0 0.2 0.4 0.6 0.8 1 1.2 Q M O C. 1.2- 1- 0.8- 0.6- 0.4- 0.2- Density 0+ 0 0.2 0.4 0.6 0.8 1 12 Q Q
Many random number generators allow users to specify the range of the random numbers to be produced. Suppose you specify that the random number Y can take any value between 0 and 6. Then the density curve of the outcomes has constant height between 0 and 6 and height O elsewhere.
Number...3...
In a probability density function such as a Normal or bell-shaped curve, the area under the curve is used to make predictions about likelihoods and probabilities. What is the area (use a proportion) under the curve from the lowest possible value to the highest possible value?
The probability density of a random variable X is given in the figure below. From this density, the probability that X is between 0.84 and 1.3 is:
Golf-course designers have become concerned that old courses are becoming obsolete since new technology has given golfers the ability to hit the ball so far. Designers, therefore, have proposed that new golf courses need to be built expecting that the average golfer can hit the ball more than 255 yards on average. Suppose a random sample of 171 golfers be chosen so that their mean driving distance is 260.4 yards, with a standard deviation of 45.9 Conduct a hypothesis test where H0:μ=255 and H1:μ>255 by computing the following: (a) test statistic ?(b) p-value p=?(c) If this was a two-tailed test, then the p-value is?
The service life T (this year) of a particular type of electric toothbrush is assumed to have the probability density f given by: see figure question (a) Find the probability that a randomly selected toothbrush (of this type) has a lifespan of more than 2 years.(b) Assume that a toothbrush of the same type has been working for one year already. What is the probability that it works for at least another 3 years?(c) What is the probability that the average lifespan of T¯ for 90 independent toothbrushes is greater than 2.1 years?
(a) Sketch the probability mass function of X . (b) Find the mean and standard deviation of the number of pots of olives sold daily. (c) If the profit obtained from selling a pot of olives is 50p, what is the expected profit made on a single day? During a working week of 6 days?
The 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. (a) Identify the graph of the uniform density function. (b) What is the probability of generating a number between 0.27 and 0.85? (c) What is the probability of generating a number greater than 0.92? (a) Choose the correct graph of the uniform density function below. A. B. Density 1.2- 1- 0.8- 606 0.6- 0.4- 0.2- 0 0.2 0.4 0.6 0.8 1 1.2 1.2- 1- 0.8- 0.6- 0.4- 0.2- 0+ Density X 0 0.2 0.4 0.6 0.8 1 1.2 (b) The probability is (c) The probability is to (Simplify your answer.) (Simplify your answer.) X C. 1.2- 1- 0.8- 0.6- 0.4- 0.2- Density 0 0.2 0.4 0.6 0.8 X 1 1.2
part (i), (ii) and (iii) is already answered. could you answer part (iv) only i. Two six-sided dice are rolled and the scores added together. Draw the sample space, the probability density function and the cumulative probability density function by hand. ii. What is the probability that the number obtained on one of the dice is a multiple of a number obtained on the other dice? What is the probability of doubles (1,1, 2,2. etc)? iii. A weekly lottery with numbers 1-49 has come up with the numbers 2,4,6,8,10 and 20,25,30,35,40 over the last month. There have been claims of fraud and the organisers are worried as ticket sales are down.Write a short paragraph on the issue giving views based on yourknowledge of probability. iv. Use six letter word to explain and illustrate the differences between permutations and combinations. Give an example where the distinction between permutations and combinations is crucial.
The 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. (a) Identify the graph of the uniform density function. (b) What is the probability of generating a number between 0.37 and 0.69? (c) What is the probability of generating a number greater than 0.83? ... OA. В. OC. Density 1.2- A Density 1.2- ADensity 1.2- 1- 1. 1- 0.8- 0.8- 0.6- 0.4- 0.2- 0+ 0.8- 0.6- 0.6- 0.4- 0.2- 04 0 0.2 0.4 0.6 0.8 1 0.4- 0.2- X 0- 0.2 0.4 0.6 0.8 1 1.2 1.2 0.2 0.4 0.6 0.8 1 1.2 (b) The probability is (Simplify your answer.) (c) The probability is (Simplify your answer.) B.

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