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.
2) Suppose we select two values x and y independently from the uniform distribution on
[0,1]. What is the probability that xy
1
2
100 identical balls are rolling along a straight line. They all have speed equal to v, but some of them might move in opposite directions. When two of them collide they immediately switch their direction and keep the speed v. What is the maximum number of collisions that can happen?
Let f(w) be a function of vector w Є RN, i.e. f(w) = 1+e Determine the first derivative and matrix of second derivatives off with respect to w.
Let A Є RN*N be a symmetric, positive definite matrix and bЄ RN a vector. If x ER, evaluate the integral Z(A,b) = e¯xAx+bx dx as a function of A and b.
John throws a fair die with faces labelled 1 to 6. ⚫ He gains 10 points if the die shows 1. ⚫ He gains 1 point if the die shows 2 or 4. • No points are allocated otherwise. Let X be the random variable describing John's gain at each throw. Determine the variance of X.
Female
Male
Totals
Less than High School
Diploma
0.077
0.110
0.187
High School Diploma
0.154
0.201
0.355
Some College/University
0.141
0.129
0.270
College/University Graduate
0.092
0.096
0.188
Totals
0.464
0.536
1.000
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