Question

Suppose that the average lifetime of a transistor is 100 working hours and that the lifetime distribution is exponential.

(a) Estimate the probability that the transistor will work at least
30 hours.

(b) Given that the transistor has functioned for 30 hours, what is
the chance that it fails in the next 25 hours.

(c) Suppose that two transistors, one in active, the other in reserve (if the primary one malfunctions, the second will be used at once). What is the chance that these two transistors remain working more than 30 hours?

Answer #1

Suppose that the average lifetime of a plane is 100 working
hours and that the lifetime distribution is exponential.
(a) Estimate the probability that the plane will work at least 50
hours.
(b) Given that the plane has functioned for 50 hours, what is the
chance that it fails in the next 25 hours.
(c) Suppose that two planes, one in active, the other in reserve
(if the primary one malfunctions, the second will be used at once).
What is...

Suppose that the average lifetime of a car is 100 working hours
and that the lifetime distribution is exponential.
(a) Estimate the probability that the car will work at least 50
hours.
(b) Given that the car has functioned for 50 hours, what is the
chance that it fails in the next 25 hours.
(c) Suppose that two cars, one in active, the other in reserve
(if the primary one malfunctions, the second will be used at once).
What is...

Suppose that the average lifetime of a plane is 100 working
hours and that the lifetime distribution is exponential.
(a) Estimate the probability that the plane will work at least 50
hours.
(b) Given that the plane has functioned for 50 hours, what is the
chance that it fails in the next 25 hours.
(c) Suppose that two planes, one in active, the other in reserve
(if the primary one malfunctions, the second will be used at once).
What is...

Engineers designing the next generation of space shuttles plan
to include two fuel pumps —one active, the other in reserve. If the
primary pump malfunctions, the second is automatically brought on
line (alpha = 2, because this is the setup for dealing with sum of
2 Exponential variables). Suppose a typical mission is expected to
require that fuel be pumped for at most 50 hours. According to the
manufacturer's specifications, pumps are expected to fail once
every 100 hours (lambda...

At a 24-hour computer repair facility broken-down computers
arrive at an average rate of 3 per day, Poisson distributed.
What is the probability that on a given day no computers arrive
for repair?
What is the probability that on a given day at least 3
computers arrive for repair?
What is the distribution of the time between arrivals of
computers to this facility and what is the average time between
arrivals?
On one particular day no computer has arrived for...

1. Suppose that a bag contains 3 red chips and 7 white chips.
Suppose that chips are drawn from the bag with replacement, i.e.
the chips are returned to the bag and shuffled before the next chip
is selected. Identify the correct statement.
a.
If many chips are selected then, in the long run, approximately
30% will be red.
b.
If ten chips are selected then three will definitely be red.
c.
If seven consecutive white chips are selected then...

2.Calculating probabilities and quantiles with RUse R and your
knowledge of the common probability densities we’ve talked about
inclass to answer the following questions.(a) A representative from
PSU’s athletic department randomly selects PSU studentsoutside the
HUB to see if they attended the last home men’s basketball game.
Letp, the probability she selects such a person, be equal to 0.001,
and letXdenotethe number of people she must survey until she finds
such a person.i. What is the probability the representative must...

Use R and your knowledge of the common probability densities
we’ve talked about inclass to answer the following questions.(a) A
representative from PSU’s athletic department randomly selects PSU
studentsoutside the HUB to see if they attended the last home men’s
basketball game. Letp, the probability she selects such a person,
be equal to 0.001, and letXdenotethe number of people she must
survey until she finds such a person.i. What is the probability the
representative must select 4 people to find...

Suppose you are a manager of a dairy farm. You are currently
milking 100 cows and each cow produces 22,000 pounds (220 cwt) of
milk per year. To produce this quantity of milk, the farm milks the
each cow twice a day (once in the morning and once in the
afternoon). Now suppose milk prices are increasing. Over the past
few months the price of milk has increased and milk is now selling
for $15/cwt. The increase in milk price...

Suppose you are a manager of a dairy farm. You are currently
milking 100 cows and each cow produces 22,000 pounds (220 cwt) of
milk per year. To produce this quantity of milk, the farm milks the
each cow twice a day (once in the morning and once in the
afternoon). Now suppose milk prices are increasing. Over the past
few months the price of milk has increased and milk is now selling
for $15/cwt. The increase in milk price...

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