The 3 month demand for a spare car part has the following probability mass function: x 0 1 2 p(x) 0.25 0.5 0.25 a) What is the probability that there will be at most 1 unit of demand during the time period? b) What is the variance of the demand?

The 3 month demand for a spare car part has the following probability mass function: x 0 1 2 p(x) 0.25 0.5 0.25 a) What is the probability that there will be at most 1 unit of demand during the time period? b) What is the variance of the demand?

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

Related questions

Q: A random variable Y has a uniform distribution over the interval (?1, ?2). Derive the variance of Y.…

Q: EX7.8) Let Y be a random variable having a uniform normal distribution such that Y~U (2,5) Find the…

Q: Components that are critical for the operation of electrical systems are replaced immediately upon…

A: 9. The given mean is 500, and standard deviation is 100. That is, μ=500,σ=100. A sample of 10…

Q: Suppose the relationship between Y and X is given by: Y = 1million + 56.43*X + error By how much…

A: The objective of the question is to find out the change in the expected value of Y when X increases…

Q: arger variance. lom variable X be the height of a random CS500 at from the same group in…

A: True

Q: The annual rate of return on an investment each year is an independent and identically distributed…

A: Given that the annual rate of return on an investment each year is an independent and identically…

Q: 36. QUESTION: Let X have the density f(x) = 2x if 0 < r <1 and f(x) = 0 otherwise. Show that X has…

Q: Let I be an indicator variable with p(I) = {p , I=1 } {1-p , I=0}. Show that the variance of I is…

A: The mean is calculated as follows: EI=∑I×PI=1×p+0×1-p=p

Q: A variable has uniform probability density function between 1 and 2. What is the expected value of…

A: Given: X~U(1,2) a=1 b=2

Q: (d) Let X P(X < 1.4)? 25 25 X;. How would you use the central limit theorem to approximate

A: We want to find the probability by using central limit theorem.

Q: 19. In Saint Tropez, the probability that it rains on a given day is 10%. Given that it rains, the…

A: f(x)=13×e−x3; x>0

Q: Find the exact mean value of X using the lowest common denominator and find the exact variance of X…

A: The pdf of random variable x is given by, fx=40-x800 ; 0≤x≤40 0 ; otherwise

Q: The lifetime of an aquatic insect has an exponential disribution with parameter θ = 10 hrs. (i)…

A: The lifetime of an aquatic insect has an exponential disribution with parameter θ = 10 hrs.

Q: There are many engineering properties which cannot be negative, and so cannot be modeled using a…

Q: (c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer…

A: Let X be the random variable that the time headway. The pdf of X is, f(x)=11x12, x>1 The cdf of…

Q: Assume that there is a rare disease. It occurs in the population at a rate of 1 per 1000; that is,…

A: The probability that the patient have positive test when disease is present is 0.95. The probability…

Q: An optical device is used to detect the passage of cars in a single lane of a downtown street.…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…

Q: f (x, y) 1 0.05 0.05 0.00 g (x) 0.10 a. Determine the mean of X. b. Determine the mean of Y. c.…

Q: Suppose the lengths of human pregnancies are normally distributed with u = 266 days and 0 = 16 days.…

A: Explanation- 1. **Given Information**: We are given that the lengths of human pregnancies follow a…

Q: a, b, d,

A: The population mean CI for a known population standard deviation is, where, The estimated…

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

The 3 month demand for a spare car part has the following probability mass function:

x	0	1	2
p(x)	0.25	0.5	0.25

a) What is the probability that there will be at most 1 unit of demand during the time period?

b) What is the variance of the demand?

Video Video

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

The time to first failure X of the software of a medical linear acceleratormay be modeled normal with μ = 1100 hours and σ = 50 hours.
2 The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second). (a) Find the probability that the demand will exceed 250 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.) (b) What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.02? (Round your answer to two decimal places.) cfs
The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 66 mg/mi. A company has 1616 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)
Let X be a normal random variable with mean 85 and a variance of 25 (i.e., X ∼ N (85, 25)). step1: Let M = aX + b for some constants a, b not equal to 0. Write an expression for the pdf of M . step 2: Suppose that X represents an approximate distribution of the final scores in a certain math course (ignore the fact that this approximation can technically have scores that are greater than 100 or less than 0). If the teacher were to curve the scores, it means he would determine a function to apply to the scores to achieve a desired distribution (assume an affine function in this case, as in the previous part). Suppose he wants the scores to be normally distributed with mean 80 and a standard deviation of 4. What should he choose for a and b? What students would see their score lowered, and what students would see their score increased?
3. The level of impurity (in percent) in the product of a certain chemical process is a random variable with probability density function 3 64 -x²(4 - x) 0 0 < x < 4 otherwise a. What is the probability that the impurity level is greater than 3%? b. What is the probability that the impurity level is between 2% and 3%? c. Find the mean impurity level. d. Find the variance of the impurity levels.
4. As fallen trees lie on the forest floor they slowly decay. Will the amount of light present have an impact on the rate of decay? In the following table x is a random variable representing the remaining percentage of total mass of a log after it was exposed to the elements for three weeks while y represents the numbers of hours of direct sunlight the log received each day. X 0.60 .70 .65 .82 .87 y 1.0 2.3 3.0 4.0 4.5 (a) Plot a scatter diagram of the data. Remember to label your axes appropriately and choose a consistent scale. (b) Based on a scatter diagram, would you estimate the correlation coefficient to be positive, close to zero, or negative? Please circle one of the following choices: A. Positive B. Close to zero C. Negative (c) Interpret your results from parts (a) and (b). 16 tv