The weekly output of a steel mill is a uniformly
distributed random variable that lies between 110 and 175 metirc
tons. 1. Compute the probability that the steel mill will produce
more than 150 metric tons next week. 2. Determine the probability
that the steel mill will produce between 120 and 160 metric tons
next week.
A random variable X is exponentially distributed with
an expected value of 50.
a-1. What is the rate parameter λ?
(Round your answer to 3 decimal places.)
a-2. What is the standard deviation of
X?
b. Compute P(44 ≤ X ≤ 56).
(Round intermediate calculations to at least 4 decimal
places and final answer to 4 decimal places.)
c. Compute P(36 ≤ X ≤ 64).
(Round intermediate calculations to at least 4 decimal
places and final answer to 4 decimal...
5. A continuous random variable X is uniformly distributed over
(0,10). Compute the probability that an observed value of X will be
within one standard deviation of its mean.
Let random variable X be uniformly distributed in interval [0,
T].
a) Find the nth moment of X about the origin.
b) Let Y be independent of X and also uniformly distributed in [0,
T]. Calculate the
second moment about the origin, and the variance of Z = X + Y
Births are approximately Uniformly distributed between the 52
weeks of the year. They can be said to follow a Uniform
distribution from 1 to 53 (a spread of 52 weeks). Round answers to
4 decimal places when possible.
The mean of this distribution is
The standard deviation is
The probability that a person will be born at the exact moment
that week 52 begins is P(x = 52) =
The probability that a person will be born between weeks 20...
A random variable X is exponentially distributed with a
mean of 0.21.
a-1. What is the rate parameter λ?
(Round your answer to 3 decimal places.)
a-2. What is the standard deviation of X?
(Round your answer to 2 decimal places.)
b. Compute P(X > 0.36).
(Round intermediate calculations to at least 4 decimal
places and final answer to 4 decimal places.)
8. A swimming pool is filled at a rate that is uniformly
distributed between 20 and 26.3 gallons per minute.
a. Draw a sketch that illustrates this particular situation.
Please label all relevant information for this probability density
function. (5 pts)
b. What is the probability that the filling rate at any one time
is between 21.3 and 24.6 gallons per minute? (6 pts)
c. What is the median rate at which this swimming pool is
filled? (4 pts) 8....
Let X and Y be independent and uniformly distributed random
variables on [0, 1]. Find the cumulative distribution and
probability density function of Z = X + Y.