Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call. Their joint probability distribution is given below: a. Find the marginal distribution g(x), x = 1, 2, 3. b. Find the marginal distribution h(y), y = 1, 3, 5. c. List the cumulative distribution function F(x)

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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The following table shows the joint probability distribution of the random variables x and y A.Are the two requirements satisfied for this joint probability distribution? Explain clearly. Showyour calculations. b. Find the marginal probability distribution of ? and graph it. Show your calculations.c. Find the marginal probability distribution of ? and graph it. Show your calculations.d. Find the correlation coefficient between ? and ?. Show your calculations.e. Comment on the direction and the strength of the association between ? and ?.f. Find the mean value of (? – ?) and the standard deviation of (? – ?). Show your calculations.
The monthly salary of all adults in a certain US town is known to be right skewed with a mean of $3700. If a random sample of 40 adults were selected from that town, what would be the shape of the distribution of the sample mean? Why? Approximately normal by the law of large numbers. Approximately normal by the central limit theorem. Right skewed because the original distribution is right skewed. O We cannot determine the shape of the distribution of the sample mean.
Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes.1. Give a mathematical expression for the probability density function of flight timeand the expected value and variance of the distribution;2. Create a scatter graph using dynamic process learnt in the previous sessions to show the uniform probability distribution graphically, then answer the below questions:a. What is the probability that the flight will be no more than 5 minutes late?b. What is the probability that the flight will be more than 10 minutes late?c. What is the probability that the flight will be between 4 and 8minutes late?d. In a month of 200 flight journeys finished, how many should have arrived 5 minutes or less earlier?Question 2 Normal DistributionNew York City is the most expensive city in the United States for lodging. The mean hotel room rate is $204 per…
Please do these 3 Qs in excel or show steps, thank you.
Consider the data set given in the accompanying table Construct a frequency marginal distribution. x1 x2 x3 Marginal distribution y1 30 25 30 enter your response here y2 30 15 50 enter your response here Marginal distribution enter your response here enter your response here enter your response here enter your response here
The owner of an automobile repair shop studied the waiting times for customers who arriveat the shop for an oil change. The following data with waiting times in minutes werecollected over a 1-month period.2 5 10 12 4 4 5 17 11 8 9 8 12 21 6 8 7 13 18 3Using classes of 0–4, 5–9, and so on, show:a. The frequency distribution.b. The relative frequency distribution.c. The cumulative frequency distribution.d. The cumulative relative frequency distribution.e. The proportion of customers needing an oil change who wait 9 minutes or less.
The table shows population statistics for the ages of Best Actor and Best Supporting Actor winners at an awards ceremony. The distributions of the ages are approximately bell-shaped. Compare the z-scores for the actors in the following situation. Best Actor Best Supporting Actor µ= 42.0 µ= 51.0 o = 8.7 o = 12 In a particular year, the Best Actor was 40 years old and the Best Supporting Actor was 77 years old. Determine the z-scores for each. Best Actor: z %3D Best Supporting Actor: z = (Round to two decimal places as needed.) Interpret the z-scores. The Best Actor was the mean, which unusual. The Best Supporting Actor was the mean, which unusual.
Calculate N and M for the following frequency distribution. X Frequency2 53 34 45 86 117 9 What are the median and mode for the frequency distribution in Q1? If a sample has a SX (sum of X) = 35 and N=7, what is the mean? Calculate N and M for the following frequency distribution. X Frequency2 93 45 89 312 218 4 What are the median and mode for the frequency distribution in Q4? If a sample has a SX (sum of X) = 56 and M=7, what is the sample size (N)? Calculate N and M for the following frequency distribution. X Frequency2 33 65 79 2What are the median and mode for the frequency distribution in Q7? If a sample has aN=16andM=4.5, what was theSX (sum of X)
The data represents the daily rainfall (in inches) for one month. Construct a frequency distribution beginning with a lower class limit of 0.00 and use a class width of 0.20. Does the frequency distribution appear to be roughly a normal distribution?
The following table displays a relative frequency distribution for the number of siblings for students in a school. For a randomly selected student in the school, let X denote the number of siblings of the student. Number of Siblings Relative Frequency 0 0.1140 1 0.1420 2 0.7010 3 0.0210 4 0.0120 5 0.0065 6 0.0025 7 0.0010 P (X < 3) = ____________ P (X = 4) = ____________
A box contains 2000 items, of which 10% are defective. Let X be the number of defectives obtained in random sample of size 10. X is hypergeometrically distributed. Note that the distribution of X can be approximated with a distribution. The mean of this approximating distribution equals
Construct a relative frequency marginal distribution. x1 x2 x3 Relative frequency marginal distribution y1 30 25 30 enter your response here y2 30 15 50 enter your response here Relative frequency marginal distribution enter your response here enter your response here enter your response here 1 (Round to three decimal places as needed.)