### 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…

Answered: The random-number generator on…

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

Which of the following is used to represent the Discrete Random Variables? a. Probability Machine Function b. Probability Density Function c. Probability Machine
Consider the joint PMF Px.x(x,y) given in the following. Pxy(x,y) | x= 0 :2 X= | (a) Find P[X=1]. (c) Find P[X>Y. (b) Find P[Y=2]. (d) Find P[Y=X+1]. 0.09 0.22 0.29 _y= 1 y= 2 0.06 0.15 0.19
Please answer this one. Thank you!
A service facility charges a $20 fixed fee plus $25 per hour of service up to 6 hours, and no additionalfee is charged for service exceeding 6 hours. Suppose that the service time r is equally likely to beany time in 0, 10 hours (Note that r is a continuous random variable). Let X represent the cost ofservice in the facility.(a) Find and sketch the cumulative distribution function for X.(b) Find and sketch the probability density function for X.(c) What is the probability that you end up paying less than $60 for service? Answer this part twodifferent ways:• Using your answer to part (b).• Finding the time (call it To) at which the service would cost exactly $60 and then finding theprobability that † < To
Example . Let the random variable X of the continuous type have the p.d.f. Ax) = 2/x, 1 < x< 0, zero elsewhere. The distribution function of X is %3D
The wait time at a popular fast food restaurant is uniformly distributed between 2 and 10 minutes on average (a) Find the probability that you wait less than 4 minutes. (b) Find the probability that you wait between 8 and 10 minutes. (c) Explain why the answers to (a) and (b) are the same. Hint: draw the probability density function for a Uniform random variable. Explain with a graph and also without a graph.
The table shows relative frequencies for red-green color blindness in one doctor's practice. M represents 'person is male' and C represents 'person is color-blind'. Use this table to find the probability P(M nC). P(Mn C) = C M M' Totals C 0.047 0.005 0.052 C' 0.392 0.556 0.948 Totals 0.439 0.561 1.000
Find out the skew and skewness of a uniform probability density function for a random variable X.
The joint probability distribution of the number X of cars and the number Y of buses per signal cycle at a proposed left-turn lane is displayed in the accompanying joint probability table. P(x, y) 1 2 0.015 0.010 0.025 1 0.030 0.020 0.050 2 0.075 0.050 0.125 3 0.090 0.060 0.150 0.060 0.040 0.100 0.030 0.020 0.050 What is the probability that there is exactly one car and exactly one bus during a cycle? What is the probability that there is at most one car and at most one bus during a cycle? What is the probability that there is exactly one car during a cycle? Exactly one bus? P(exactly one car) = P(exactly one bus) = - Suppose the left-turn lane is to have a capacity of five cars and one bus is equivalent to three cars. What is the probability of an overflov during a cycle?
The probability that a randomly selected home has a garage space for 0, 1, 2, 3 cars are 0.22, 0.33, 0.37, and 0.08, respectively. a) Construct a probability distribution for the data. Garage Space, X ♥ P(x) 0.22 0.33 0.37 0.08 b) Calculate E(X) (same as µ), o“, and o. .2 Round to two decimal places. Population Mean: 1.31 %3D Population Standard Deviation: o Population Variance: %3D c) What does the population mean tell us about this problem? If we look at many homes, we expect to see on average about 1.31 garage spaces. d) What does the population standard deviation tell us about this problem? If we look at many homes, we expect the variation to be about 0.90 garage spaces. 3. II 2.
Tesla Battery Recharge Time. The electric-vehicle manufacturing company Tesla estimates that a driver who commutes 50 miles per day in a Model Swill require a nightly charge time of around 1hour and 45 minutes (105 minutes) to recharge the vehicle's battery (Tesla company website). Assume that the actual recharging time required is uniformly distributed between 90 and 120 minutes. a. Give a mathematical expression for the probability density function of battery recharging time for this b. What is the probability that the recharge time will be less than 110 minutes? c. What is the probability that the recharge time required is at least 100 minutes? d. What is the probability that the recharge time required is between 95 and 110 minutes?
1. or a cumulative distribution funetion (cdf). Decide if the function graphed below is a probability density function (pdf) 2c 4 8.

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS