There are 10 independent and identical internet servers each having a 0.89 steady-state probability (availability) of...
There are 10 independent and identical internet servers each having a 0.89 steady-state probability (availability) of operating. What is the probability that AT LEAST seven will be available at any given time? Hint: consider the binomial distribution.
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There are 10 independent and identical internet servers each
having a 0.89 steady-state probability (availability) of...
10. The length of time for one individual to be served at a cafeteria is a...
10. The length of time for one individual to be served at a cafeteria is a random variable having an exponential distribution with a mean of 4 minutes. (a) What is the probability that a person is served in less than 3 minutes? (b) What is the probability that a person is served in less than 3 minutes on at least 4 of the next 6 days? (Hint: use binomial distribution.)
Imagine you are the network administrator of University X having 10 campuses in Towson, Maryland. You want to build a connected network of servers (each server is either a regular or a routing one), o...
Imagine you are the network administrator of University X having 10 campuses in Towson, Maryland. You want to build a connected network of servers (each server is either a regular or a routing one), one at each campus, and want to choose some of them to be the designated routing servers. A routing server will serve regular servers who connect directly to it via high speed cables, and every regular server must connect to at least one routing server. Your...
I need help with questions 2 and 3 Each outcome may be člassifled a ee success...
I need help with questions 2 and 3
Each outcome may be člassifled a ee success The binomial random variable is continuous. OI d) 2. A discrete random variable, X, has the following probability distribution: PCX .1 1 .2 2 4 3 .3 (a) What is the probability that X is not more than 1? (b) What is the probability that X is at least 2? (c) What is the mean of X? (d) What is the standard deviation of...
2B i The binomial probability distribution P(r:p;n) is given by n! What does this distribution describe? State the...
2B i The binomial probability distribution P(r:p;n) is given by n! What does this distribution describe? State the meaning of the following three terms in the distribution 131 (n-F! A single perfect dice is rolled multiple times Calculate the probability of throwing two fives with 2 throws of the dice. 2 Calculate the probability of obtaining one five and one six in any order from2 throws of the dice. 3 How often does one need to roll the dice to...
Problem 2: Consider a sequence of independent trials each having a probability p (with 0 <...
Problem 2: Consider a sequence of independent trials each having a probability p (with 0 < p < 1) of selecting some household whose wealth exceeds 100 Million dollars. Let X denote the number of trials it takes to observe some household whose wealth exceeds 100 Million dollars. (a) Find the support of X. (b) Find the PDF of X (c) Suppose p = 0.01. How many trials can you expect for finding some household whose wealth exceeds 100 Million...
A datacenter has 10 servers and 4 routers, which they want to connect. Each server and each route...
A datacenter has 10 servers and 4 routers, which they want to connect. Each server and each router can have any number of cables attached to it. Suppose that they would like the connections to satisfy the following property: at any given time, if no more than 4 servers are transmitting data, then each server can transmit via a separate router. For that, they want every (sub)set of 4 to have cables going to all four routers. What is the...
(3). How is the steady state probability distribution changed? Problem 2 There are three machines...
(3). How is the steady state probability distribution changed? Problem 2 There are three machines and two mechanics in a factory. The break time of each machine is exponentially distributed with A1 (per day). The repair time of a broken machine is also exponentially distributed with a mean of 3 hours. (Mechanics work separately). (1). Construct the rate diagram for this queueing system. (be careful about the arrival rate An (2). Set up the rate balance equations, then solve for...
Consider an random variable A generated from two independent, non-identically distributed rvs, B and C: Here...
Consider an random variable A generated from two independent,
non-identically distributed rvs, B and C:
Here we would say that A has a zero-inflated binomial
distribution, which is like a binomial but with a spike at zero.
This is a type of mixture, since any given realization of A can be
viewed as having come from one of a number of distinct
distributions, in this case either a zero-only distribution or a
binomial.
Write out an expression for the probabilty...
Consider a family with eight children. Assuming that the sex each child is determined independently of the others and that each child is equally likely to be female or male,
Consider a family with eight children. Assuming that the sex each child is determined independently of the others and that each child is equally likely to be female or male, a. What is the probability that exactly four children are female? Hint: Use the binomial distribution. (10 points) b. What is the probability that at most seven children are female? Hint: What is the complement of this event? (10 points)c. Find the conditional probability that the first two children born are female...
An average of 10 cars/hour arrive at a car repair station with two servers. Assume that the avera...
An average of 10 cars/hour arrive at a car repair station with two servers. Assume that the average service for each customer is 4 minutes and both interarrival and service times are exponentially distributed. If this car repair station has a capacity of 4 cars a. Write the steady-state equations and solve them. Compare the results with those calculated in question 1 and draw a conclusion. b. What is the probability that the car repair station is idle? c. What...
10. The length of time for one individual to be served at a cafeteria is a random variable having an exponential distribution with a mean of 4 minutes. (a) What is the probability that a person is served in less than 3 minutes? (b) What is the probability that a person is served in less than 3 minutes on at least 4 of the next 6 days? (Hint: use binomial distribution.)
I need help with questions 2 and 3
Each outcome may be člassifled a ee success The binomial random variable is continuous. OI d) 2. A discrete random variable, X, has the following probability distribution: PCX .1 1 .2 2 4 3 .3 (a) What is the probability that X is not more than 1? (b) What is the probability that X is at least 2? (c) What is the mean of X? (d) What is the standard deviation of...
2B i The binomial probability distribution P(r:p;n) is given by n! What does this distribution describe? State the meaning of the following three terms in the distribution 131 (n-F! A single perfect dice is rolled multiple times Calculate the probability of throwing two fives with 2 throws of the dice. 2 Calculate the probability of obtaining one five and one six in any order from2 throws of the dice. 3 How often does one need to roll the dice to...
Problem 2: Consider a sequence of independent trials each having a probability p (with 0 < p < 1) of selecting some household whose wealth exceeds 100 Million dollars. Let X denote the number of trials it takes to observe some household whose wealth exceeds 100 Million dollars. (a) Find the support of X. (b) Find the PDF of X (c) Suppose p = 0.01. How many trials can you expect for finding some household whose wealth exceeds 100 Million...
(3). How is the steady state probability distribution changed? Problem 2 There are three machines and two mechanics in a factory. The break time of each machine is exponentially distributed with A1 (per day). The repair time of a broken machine is also exponentially distributed with a mean of 3 hours. (Mechanics work separately). (1). Construct the rate diagram for this queueing system. (be careful about the arrival rate An (2). Set up the rate balance equations, then solve for...
Consider an random variable A generated from two independent,
non-identically distributed rvs, B and C:
Here we would say that A has a zero-inflated binomial
distribution, which is like a binomial but with a spike at zero.
This is a type of mixture, since any given realization of A can be
viewed as having come from one of a number of distinct
distributions, in this case either a zero-only distribution or a
binomial.
Write out an expression for the probabilty...
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