Question
In: Statistics and Probability
Lifetime of a particular laptop is exponential random variable with average of 5 years. A company...
Lifetime of a particular laptop is exponential random variable with average of 5 years. A company orders 100 of such laptops. Find the probability that there are more than 20 laptops still in operation after 6 years from the date of purchase. (Hint: First compute the probability of one laptop still being in operation after 6 years. That will be the probability of ”success”. Then compute the probability that you’ve at least 20 out of 100 with that property.)
Solutions
orchestra answered 2 years agoRelated Solutions
The lifetime of a particular bulb is a random variable with an average of μ =...
The lifetime of a particular bulb is a random variable with an
average of μ = 2000 hours and a standard deviation of σ = 200
hours.
(c) Calculate the probability that a bulb will last more than
2300 hours if it lasts longer than 2100 hours.
(d) Calculate the probability that a bulb will last less than 2150
hours if it has lasted more than 2050 hours.
The lifetime of a particular bulb is a random variable with an average of μ =...
The lifetime of a particular bulb is a random variable with an
average of μ = 2000 hours and a standard deviation of σ = 200
hours.
(a) What is the probability that a bulb has a lifetime between
2000 and 2400 hours?
(b) What is the probability that a bulb will last less than 1470
hours?
(c) In the case that a bulb lasts for more than 2100 hours, the
probability that it will last more than 2300 hours...
For a particular machine, its useful lifetime (random variable T) is modeled by an exponential probability...
For
a particular machine, its useful lifetime (random variable T) is
modeled by an exponential probability density function. Given that
the expected lifetime of this machine is 10 years, find the
exponential probability density function f(t) for random variable
T
For a particular machine, its useful lifetime (random variable T) is modeled by an exponential probability...
For
a particular machine, its useful lifetime (random variable T) is
modeled by an exponential probability density function. Given that
the expected lifetime of this machine is 10 years, find the
exponential probability density function f(t) for random variable
T
Suppose X is an exponential random variable with mean 5 and Y is an exponential random...
Suppose X is an exponential random variable with mean 5 and Y is
an exponential random variable with mean 10. X and Y are
independent. Determine the coefficient of variation of X + Y
The time required to service a particular machine is an exponential random variable with mean 10...
The time required to service a particular machine is an
exponential random variable with mean 10 minutes. If a repair
person has 35 machines to service, compute the approximate
probability that all the work can be completed in under 5
hours.
The usable lifetime of a particular electronic component is known to follow an exponential distribution with...
The usable lifetime of a particular electronic component is
known to follow an exponential distribution with a mean of 6.1
years. Let X = the usable lifetime of a randomly selected
component. (a) The proportion of these components that have a
usable lifetime between 5.9 and 8.1 years is __. (b) The
probability that a randomly selected component will have a usable
life more than 7.5 years is __. (c) The variance of X is __.
Suppose the waiting time between earthquakes in B is an exponential random variable. On average, B...
Suppose the waiting time between earthquakes in B is an
exponential random variable. On average, B gets a really bad
earthquake every 100 years. Given that the last really bad
earthquake was 99 years ago, compute the probability we get a
really bad earthquake within one year from now.
Answer is 0.00995
Q1. (A) Explain the exponential random variable and normal random variable with at-least ten examples in...
Q1.
(A) Explain the exponential random variable and normal random
variable with at-least ten examples in real life? In which
situation we prefer normal random variable instead of exponential
variable?
(B) Find the Mean, variance and cumulative density function for
following probability density function as: (state your results in
detail computation)
f(w)=10
e-10w ; 0≤w≤∞
5) The lifetime of a certain type of batteries follows an exponential distribution with the mean...
5) The lifetime of a certain type of batteries follows an
exponential distribution with the mean of 12 hours.
a) What is the probability that a battery will last more than
14 hours?
b) Once a battery is depleted, it is replaced with a new
battery of the same type. Assuming independence between lifetimes
of batteries, what is the probability that exactly 2 batteries will
be depleted within 20 hours?
c) What is the probability that it takes less than...
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