Question
In: Statistics and Probability
(a) Give the definition of memoryless for a random variable X. (b) Show that if X...
(a) Give the definition of memoryless for a random variable X. (b) Show that if X is an exponential random variable with parameter λ , then X is memoryless. (c) The life of the brakes on a car is exponentially distributed with mean 50,000 miles. What is that probability that a car gets at least 70,000 miles from a set of brakes if it already has 50,000 miles?
Solutions
orchestra answered 1 year agoRelated Solutions
1. (Memoryless property) [10] Consider a discrete random variable X ∈ N (X ∈ N is...
1. (Memoryless property) [10]
Consider a discrete random variable X ∈ N (X ∈ N is a convention
to represent that the range of X is N). It is memoryless if
Pr{X > n + m|X > m} = Pr{X > n}, ∀m,n ∈{0,1,...}.
a) Let X ∼ G(p), 0 < p ≤ 1. Show that X is memoryless.
[2]
b) Show that if a discrete positive integer-valued random
variable X is memoryless, it must be a geometric random variable,...
(a) Give a definition of a closed set. (b) Show, directly from the definition, that a...
(a) Give a definition of a closed set.
(b) Show, directly from the definition, that a union of finitely
many closed sets is closed.
(c) Give an example of a countable collection of closed
intervals In such that ∪ n=1 to ∞ In is open (make sure
to prove it).
explain why memoryless property does not apply to the binomial random variable
explain why memoryless property does not apply to the binomial
random variable
Determine whether or not the random variable X is a binomial random variable. If so, give...
Determine whether or not the random variable X is a binomial
random variable. If so, give the values of n and p. If not, explain
why not.
a. X is the number of dots on the top face of fair die that is
rolled.
b. X is the number of hearts in a five-card hand-drawn (without
replacement) from a well-shuffled ordinary deck.
c. X is the number of defective parts in a sample of ten randomly
selected parts coming from...
Identify the Distribution Select the Distribution that best fits the definition of the random variable X...
Identify the Distribution
Select the Distribution that best fits the definition of the
random variable X in each case.
Each hurricane independently has a certain probability
of being classified as "serious." A climatologist wants to study
the effects of the next 5 serious hurricanes. X = the number of
non-serious hurricanes observed until the data is
collected.
Discrete Uniform
Hypergeometric
Binomial
Negative Binomial
Geometric
Poisson
Continuous Uniform
Exponential
Normal
Multinomial
None of the Above
Ten percent of Netflix users watch...
Identify the Distribution Select the Distribution that best fits the definition of the random variable X...
Identify the Distribution
Select the Distribution that best fits the definition of
the random variable X in each case.
Question 1) You have 5 cards in a pile, including one
special card. You draw 3 cards one at a time without replacement. X
= the number of non-special cards drawn.
Discrete Uniform
Hypergeometric
Binomial
Negative Binomial
Geometric
Poisson
Continuous Uniform
Exponential
Normal
Multinomial
None of the Above
Question 2) The number of car accidents at a particular
intersection occur independently...
Identify the Distribution Select the Distribution that best fits the definition of the random variable X...
Identify the Distribution
Select the Distribution that best fits the definition of
the random variable X in each case.
Question 1) In a single game of (American) roulette, a
small ball is rolled around a spinning wheel in such a way that it
is equally likely to land in any of 38 bins. Sixteen of the bins
are Red, another 16 are Black, and the remaining 2 are Green.
Suppose 5 games of roulette are to be played. What is...
Show that the cumulative distribution function for a random variable X with a geometric distribution is...
Show that the cumulative distribution function for a random
variable X with a geometric distribution is
F(x) = 0 for x < 0,
F(x) = p for 0 <= x < 1,
and, in general, F(x)= 1 - (1-p)^n for n-1 <= x < n for n
= 2,3,....
Determine whether or not the random variable X is a binomial random variable. (a) X is...
Determine whether or not the random variable X is a binomial
random
variable.
(a)
X is the number of dots on the top face of a fair die
(b)
X is the number of hearts in a five card hand drawn (without
replacement) from a well
shuffled ordinary deck.
(c)
X is the number of defective parts in a sample of ten randomly
selected parts coming from a manufacturing process in which 0.02%
of all parts are defective.
(d)
X...
give an example of a discrete random variable X whose values are integers and such that...
give an example of a discrete random variable X whose values are
integers and such that E(X) = infinite. Prove that E(X) = infinite
for your example. (hints: if you will be paid 2^k dollars for the
kth head when you flip a fair coin., the expected value is
infinite...) Or give other easy examples.
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