There are two possible causes for a breakdown of a machine. To check the first possibility would cost C 1 dollars, and, if that were the cause of the breakdown, the trouble could be repaired at a cost of R 1 dollars. Similarly, there are costs C 2 and R 2 associated with the second possibility. Let p and 1 − p denote, respectively, the probabilities that the breakdown is caused by the first and second possibilities. Under what conditions on p , C i , R i , i = 1 , 2 , should we check the first possible cause of breakdown and then the second, as opposed to reversing the checking order, so as to minimize the expected cost involved in returning the machine to working order? Note: If the first check is negative, we must still check the other possibility.
There are two possible causes for a breakdown of a machine. To check the first possibility would cost C 1 dollars, and, if that were the cause of the breakdown, the trouble could be repaired at a cost of R 1 dollars. Similarly, there are costs C 2 and R 2 associated with the second possibility. Let p and 1 − p denote, respectively, the probabilities that the breakdown is caused by the first and second possibilities. Under what conditions on p , C i , R i , i = 1 , 2 , should we check the first possible cause of breakdown and then the second, as opposed to reversing the checking order, so as to minimize the expected cost involved in returning the machine to working order? Note: If the first check is negative, we must still check the other possibility.
Solution Summary: The author explains how to find a condition on p,C_i, Rs, and i=1,2 that is required to minimize the expected cost involved
There are two possible causes for a breakdown of a machine. To check the first possibility would cost
C
1
dollars, and, if that were the cause of the breakdown, the trouble could be repaired at a cost of
R
1
dollars. Similarly, there are costs
C
2
and
R
2
associated with the second possibility. Let p and
1
−
p
denote, respectively, the probabilities that the breakdown is caused by the first and second possibilities. Under what conditions on
p
,
C
i
,
R
i
,
i
=
1
,
2
,
should we check the first possible cause of breakdown and then the second, as opposed to reversing the checking order, so as to minimize the expected cost involved in returning the machine to working order?
Note: If the first check is negative, we must still check the other possibility.
Please solve the following Statistics and Probability Problem (show all work) :
The probability that a patient recovers from a rare blood disease is 0.4 and 10 people are known to havecontracted this disease. Let X denote the random variable which denotes the number of patient who survivefrom the disease.1. Plot the probability mass function (pmf) of X.2. Plot the cumulative distribution function (cdf) of X.3. What is the probability that at least 8 survive, i.e., P {X ≥ 8}?4. What is the probability that 3 to 8 survive, i.e., P {3 ≤ X ≤ 8}?
Please solve the following Probability and Statistics problem (show all work and double check solution is correct):
Suppose that a die is rolled twice. What are the possible values that the following random variables can take1. the maximum value to appear in the two rolls;2. the value of the first roll minus the value of the second roll?3. Calculate the probabilities associated with the above two random variables?
Please solve the following statistics and probability problem (show all work) :
This problem is to show that determining if two events are independent is not always obvious.1. Consider a family of 3 children. Consider the following two events. A is the event that the familyhas children of both sexes and B is the event that there is at most one girl. Are events A and Bindependent?2. What is the answer in a family with 4 children?
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.
Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License