Problem 4: The number of breakdowns of a machine is a random variable with λ =...
Problem 4: The number of breakdowns of a machine is a random variable with λ = 2.2 breakdowns per month. Find the probability that the machine will work during any given month with:
- No breakdowns
- One breakdown
- Two breakdowns
- At least two breakdowns
- What is the expected value for the distribution
- What is the standard deviation for the distribution
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Problem 4: The number of breakdowns of a machine is a random
variable with λ =...
The number of breakdowns Y per day for a certain machine is a Poisson random variable with mean A...
The number of breakdowns Y per day for a certain machine is a Poisson random variable with mean A. The daily cost of repairing these breakdowns is given by C 3Y2. If Y, Y2, Y denote the observed number of breakdowns for n independently selected days, find an MVUE for E(C).
The number of breakdowns Y per day for a certain machine is a Poisson random variable with mean A. The daily cost of repairing these breakdowns is given by...
1. The number of breakdowns of a computer network follows a Poisson process with rate α...
1. The number of breakdowns of a computer network follows a Poisson process with rate α = 0.2 breakdowns per week. This means the number of breakdowns during a period of t weeks is a Poisson random variable with parameter λ = 0.2t. (a) What is the probability that exactly 3 breakdowns are to occur during a 10-week period? (b) What is the probability that at least 2 breakdowns are to occur in next 10 weeks? (c) How many breakdowns...
C1: Snow Manufacturing Co. has 6 machines that perform a particular task. Breakdowns occur frequently for this machine. Past records indicate that the number of breakdowns that occur each day is d...
C1: Snow Manufacturing Co. has 6 machines that perform a particular task. Breakdowns occur frequently for this machine. Past records indicate that the number of breakdowns that occur each day is described by the following probability distribution: SK2: 5 marks Number of Probability Breakdowns 0.2 0.3 0.4 More than 3 0.0 Required: 1. What is the expected number of breakdowns in any given day? (2 marks) 2. What is the variance for this distribution? (1 mark) 3. What is the...
3. The time in days between breakdowns of a machine is exponentially distributed with λ-02 a....
3. The time in days between breakdowns of a machine is exponentially distributed with λ-02 a. What is the expected time between machine breakdowns? b. What is the probability that after the machine is repaired, it lasts at least five days before failing again? C. If the machine has performed satisfactorily for seven days, what is the probability that it lasts nine days before breaking down?
The maintenance department in a factory claims that the number of breakdowns of a particular machine...
The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of 4 breakdowns every 384 hours. Let x denote the time (in hours) between successive breakdowns. (a) Find λ and μx. (Write the fraction in reduced form.) (b) Write the formula for the exponential probability curve of x. (d) Assuming that the maintenance department's claim is true, find the probability that the time between successive breakdowns is...
1 The life (in years) of a certain machine is a random variable with probability density...
1 The life (in years) of a certain machine is a random variable with probability density function defined by f(x) = 5 + 2 vx for x in (1, 25). 136 A. Find the mean life of this machine. The mean life is approximately years. (Round to two decimal places as needed.) B. Find the standard deviation of the distribution. The standard deviation is approximately years. (Round the final answer to two decimal places as needed. Use the expected value...
1. Let the random variable X represent the number of defective parts for a machine when...
1. Let the random variable X represent the number of defective parts for a machine when 3 parts are sampled from a production line and tested. The following is the probability distribution of X 0 1 T0.38 2 3 х 0.10 0.01 0.51 (a) Compute expected value of the random variable X c) ) S 0. the l (b) Compute standard deviation of the random variable X (c) If g(X) = 2X +3, what is the expected value of g(X)?...
a) (8 points) The number of breakdowns Y per day for a certain machine is a...
a) (8 points) The number of breakdowns Y per day for a certain machine is a Poisson random variable with mean 1. The daily cost of repairing these breakdowns is given by C = 3Y2. If Y1, ..., Yn denote the observed number of breakdowns for n independently selected days, find and MVUE for E(C). b) (7 points) A random sample Y1, ..., Yn is selected from a population of Uniform(0,0) random variables. Is the estimator Ô = 27 a...
Problem 3: The number of breakdowns of a system for the past 30 months is given...
Problem 3: The number of breakdowns of a system for the past 30 months is given in the table below. Each breakdown costs 500 dollars. Instead if an outside company does preventive maintenance on the system, the breakdowns reduce to 2 per month. This outside company charges 500 dollars per month for their service. Shall we contract out to them or not? # of breakdowns # of months that breakdowns occurred 0 6 2 3 4 5 5 5 3...
The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson...
The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of 3 breakdowns every 588 hours. Let x denote the time (in hours) between successive breakdowns. (a) Find and ux. (Write the fraction in reduced form.) = My = (b) Write the formula for the exponential probability curve of x. f(x) = 1 e-x/ for x 2 (d) Assuming that the maintenance department's claim is true, find...
The number of breakdowns Y per day for a certain machine is a Poisson random variable with mean A. The daily cost of repairing these breakdowns is given by C 3Y2. If Y, Y2, Y denote the observed number of breakdowns for n independently selected days, find an MVUE for E(C).
The number of breakdowns Y per day for a certain machine is a Poisson random variable with mean A. The daily cost of repairing these breakdowns is given by...
C1: Snow Manufacturing Co. has 6 machines that perform a particular task. Breakdowns occur frequently for this machine. Past records indicate that the number of breakdowns that occur each day is described by the following probability distribution: SK2: 5 marks Number of Probability Breakdowns 0.2 0.3 0.4 More than 3 0.0 Required: 1. What is the expected number of breakdowns in any given day? (2 marks) 2. What is the variance for this distribution? (1 mark) 3. What is the...
3. The time in days between breakdowns of a machine is exponentially distributed with λ-02 a. What is the expected time between machine breakdowns? b. What is the probability that after the machine is repaired, it lasts at least five days before failing again? C. If the machine has performed satisfactorily for seven days, what is the probability that it lasts nine days before breaking down?
1 The life (in years) of a certain machine is a random variable with probability density function defined by f(x) = 5 + 2 vx for x in (1, 25). 136 A. Find the mean life of this machine. The mean life is approximately years. (Round to two decimal places as needed.) B. Find the standard deviation of the distribution. The standard deviation is approximately years. (Round the final answer to two decimal places as needed. Use the expected value...
1. Let the random variable X represent the number of defective parts for a machine when 3 parts are sampled from a production line and tested. The following is the probability distribution of X 0 1 T0.38 2 3 х 0.10 0.01 0.51 (a) Compute expected value of the random variable X c) ) S 0. the l (b) Compute standard deviation of the random variable X (c) If g(X) = 2X +3, what is the expected value of g(X)?...
a) (8 points) The number of breakdowns Y per day for a certain machine is a Poisson random variable with mean 1. The daily cost of repairing these breakdowns is given by C = 3Y2. If Y1, ..., Yn denote the observed number of breakdowns for n independently selected days, find and MVUE for E(C). b) (7 points) A random sample Y1, ..., Yn is selected from a population of Uniform(0,0) random variables. Is the estimator Ô = 27 a...
Problem 3: The number of breakdowns of a system for the past 30 months is given in the table below. Each breakdown costs 500 dollars. Instead if an outside company does preventive maintenance on the system, the breakdowns reduce to 2 per month. This outside company charges 500 dollars per month for their service. Shall we contract out to them or not? # of breakdowns # of months that breakdowns occurred 0 6 2 3 4 5 5 5 3...
The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of 3 breakdowns every 588 hours. Let x denote the time (in hours) between successive breakdowns. (a) Find and ux. (Write the fraction in reduced form.) = My = (b) Write the formula for the exponential probability curve of x. f(x) = 1 e-x/ for x 2 (d) Assuming that the maintenance department's claim is true, find...
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