Suppose that a die is rolled twice. Let X be the minimum value to appear in the tworolls.(a)Construct the table of the probability mass function of X. Demonstrate howyou obtained the probability values for each value of X.(b)Obtain the distribution function of X.(c)Write out the moment generating function. Hence, compute the mean.(d)Justify your answer in (c) using the basic definition of the mean.(e)Using the second factorial moment of X, compute the variance.

Given: A die that is rolled twice. The minimum value to appear in two rolls=X To construct: To…

Answered: Suppose that a die is rolled twice. Let…

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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For each probability expression, find the unknown z- value(s). Unless directed otherwise, use three decimals in your answers. (a) P(Z ≤ zo) = 0.86. Find zo. 20 (b) P(Z ≤ zo) = 0.24. Find zo. 20 = 20 (c) P(Z ≥ zo) = 0.4. Find zo. = 20 = (c) P(z0 ≤ Z ≤ 0.64) = 0.5988. Find zo. = (use two decimals)
Show work for every step. Two types of customers (Preferred and Regular) call a service center. Preferred customers call with rate 3 per hour, and Regular customers call with rate 5 per hour. The interarrival times of the calls for each customer type are exponentially distributed. If the call center opens at 8:00 AM, what is the probability that the first call (regardless of customers type who calls) is received before 8:15 AM?
In an uncertain economy, Americans tend to keep spending down. Let x be the amount of money U.S. individuals spend on groceries monthly. Suppose the probability distribution of x is a uniform distribution from $300 to $400 which is represented by the picture below. f(x) 0.010 0.008 0.006 0.004 0.002 300 320 340 360 380 400 X i (a) What is the probability that a randomly selected individual spends between $315 and $370 on groceries each month? (b) Determine whether the following statement is true or false. The variable, the amount an individual plans to spend on groceries per month, is a numerical (quantitative) variable. True O False
Determine the value of c such that the function is a probability mass function. g= {(11,0.12), (13,0.4c), (15,0.4c), (17,0.22)} ... C = (Simplify your answer.)
Fill in the P(X=x)values to give a legitimate probability distribution for the discrete random variable X, whose possible values are −2,1, 3, 4, and 5.
The probability distribution given below represents the projected profit (in thousands of dollars) earned from a business over a year. Profit (x) in thousands of dollars f(x) -100 0.05 -50 0.15 0 0.30 50 0.35 100 0.12 200 0.03 a.) What is the probability that the business will operate at a loss for the year? b.) What is the probability that the business will break even? c.) What is the expected value for profit? Fill out the table below to help you calculate the value.
(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?
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.
In each case, determine the value of the constant c that makes the probability statement correct. (Round your answers to two decimal places.) USE SALT (a) (c) = 0.9857 2.189 (b) P(0 ≤Z≤ c) = 0.3133 0.89 (c) P(C ≤ Z) = 0.1335 1.11 You may need to use the appropriate table in the Appendix of Tables to answer this question.

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