by the formula The expectation of the number of defective devices is given P T = N[1 − (1 – 2²N)”]· - - where P is the probability that the trial of one device is considered successful, is the average number of successful trials until the first failure occurs, N is the number of devices tested and m is the number of trials (successes and failures) for each device. Using the linearization method, find the dependence of the expectation and variance of the random variable T on m if N, P and 2 are independent random variables, whose expectations and variances are: M[N] = 5, M[P] = 0.8, Μ[Ω] = 4, D[N] = 1, D[P] = 0.1, D[P] = 0.2.
by the formula The expectation of the number of defective devices is given P T = N[1 − (1 – 2²N)”]· - - where P is the probability that the trial of one device is considered successful, is the average number of successful trials until the first failure occurs, N is the number of devices tested and m is the number of trials (successes and failures) for each device. Using the linearization method, find the dependence of the expectation and variance of the random variable T on m if N, P and 2 are independent random variables, whose expectations and variances are: M[N] = 5, M[P] = 0.8, Μ[Ω] = 4, D[N] = 1, D[P] = 0.1, D[P] = 0.2.
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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![by the formula
The expectation of the number of defective devices is given
- N[₁ - (1 - 2N)"]·
ΩΝ
T =
where P is the probability that the trial of one device is considered successful,
is the average number of successful trials until the first failure occurs, N is the
number of devices tested and m is the number of trials (successes and failures)
for each device.
Using the linearization method, find the dependence of the expectation
and variance of the random variable T on m if N, P and 2 are independent
random variables, whose expectations and variances are:
M[N] = 5,
M[P] = 0.8,
Μ[Ω] = 4,
D[N] = 1,
D[P] = 0.1,
D[P] = 0.2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab82f132-66ae-4e4f-a004-2a580bf28595%2F192a3117-6117-4255-8ac5-69ba0722fead%2F3ott4ld_processed.jpeg&w=3840&q=75)
Transcribed Image Text:by the formula
The expectation of the number of defective devices is given
- N[₁ - (1 - 2N)"]·
ΩΝ
T =
where P is the probability that the trial of one device is considered successful,
is the average number of successful trials until the first failure occurs, N is the
number of devices tested and m is the number of trials (successes and failures)
for each device.
Using the linearization method, find the dependence of the expectation
and variance of the random variable T on m if N, P and 2 are independent
random variables, whose expectations and variances are:
M[N] = 5,
M[P] = 0.8,
Μ[Ω] = 4,
D[N] = 1,
D[P] = 0.1,
D[P] = 0.2.
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