let X be a random variable that denotes the life (or time to
failure) in hours...
let X be a random variable that denotes the life (or time to
failure) in hours of a certain electronic device. Its probability
density function is given by
f(x){ 0.1 e−0.1x, x > 0 , 0 , elsewhere
(a) What is the mean lifetime of this type of device?
(b) Find the variance of the lifetime of this device.
(c) Find the expected value of X2 − 20X + 100.
1. For which type of continuous distribution are the mean and
the median always the same?...
1. For which type of continuous distribution are the mean and
the median always the same?
uniform and normal distributions only
all of the above
uniform distribution
exponential distribution
normal distribution
2. The skewness of a normal distribution is:
negative
zero
positive
something that varies
3. The standard normal probability distribution has a mean of
______ and a standard deviation of ______.
0, 1
1, 0
1, 1
0, 0
4. Any normal probability distribution can be converted to a...
Note: The following problem involves the concept that if X~
Exponential(λ) then the expected value (also...
Note: The following problem involves the concept that if X~
Exponential(λ) then the expected value (also referred to as average
or mean) of X is 1 / λ. Conversely, λ = 1 / average. Once you know
the value of λ, you also know the PDF and CDF which can be used to
calculate the required probabilities.
The number of days ahead travelers purchase their airline
tickets can be modeled by an exponential distribution with the
average amount of time...
1. (a) Y1,Y2,...,Yn form a random sample from a probability
distribution with cumulative distribution function FY...
1. (a) Y1,Y2,...,Yn form a random sample from a probability
distribution with cumulative distribution function FY (y) and
probability density function fY (y). Let Y(1) = min{Y1,Y2,...,Yn}.
Write the cumulative distribution function for Y(1) in terms of FY
(y) and hence show that the probability density function for Y(1)
is fY(1)(y) = n{1−FY (y)}n−1fY (y). [8 marks]
(b) An engineering system consists of 5 components connected in
series, so, if one components fails, the system fails. The
lifetimes (measured in...
Data
For Tasks 1-8, consider the following data:
7.2, 1.2, 1.8, 2.8, 18, -1.9, -0.1, -1.5,...
Data
For Tasks 1-8, consider the following data:
7.2, 1.2, 1.8, 2.8, 18, -1.9, -0.1, -1.5, 13.0, 3.2, -1.1,
7.0, 0.5, 3.9, 2.1, 4.1, 6.5
In Tasks 1-8 you are asked to conduct some computations
regarding this data. The computation should be carried out
manually. All the steps that go into the computation should be
presented and explained. (You may use R in order to verify your
computation, but not as a substitute for conducting the manual
computations.)
A Random...