There are two stoks on the market, stock A and stock B. Every day the price of stock A will either increase by 1 dollar with probability 0.6 or decrease by one dollar with probability 0.4. Similarly stock B will either increase by 2 dollars with probability 0.55 or decrease by two dollars with probability 0.45.
A circuit is composed by two devices, A and B, connected in parallel (see figure).
You know that the circuit fails if both devices fail and that each device has a exponential life time with parameter λ, this means that if T_{A} and T_{B} are the r.v. describing the lifetime of device A and B respectively then both T_{A} and T_{B} are exponential r.v. with parameter λ.
You observe the lifetime of 10 such circuits and obtain the following breacking-down times:
3.47 1.69 1.78 0.45 1.60 3.91 2.81 7.66 0.72 2.32
(Bonus) The following data come from a population uniformly distributed between - A and A:
-0.255 0.915 -0.185 -0.363 0.508 -0.559 1.436 1.013 1.251 -0.539
Among the sudent that attempted the exams of Calculus III (CIII) and Differential Equation (DE) is oberved that the joint probability of passing or failing the exams is given by the following table:
CIII | |||||
f | p | ||||
DE | f | 0.3 | 0.1 | ||
p | 0.1 | 0.5 |
This means, for example, that the probability for a student to pass both exams is 0.5 while the probability of passing DE and failing CIII is 0.1. Given a student, let X be the r.v. that describes his result in DE and Y the r.v. that describes his result in CIII. Both variables take value 0 or 1 where 0 mean fail and 1 pass.