Consider patients coming to a doctor's office at random point in time. Let X, denote the time (in hrs) that the nth patient has to wait before being admitted to see the doctor. Describe the random process X₁, n 21 A random process is defined by X(t)=T+(1-1) where T'is uniform random variable in (0, 1) Find the CDF of X(t) b. Find E(X(t)) and Cxx (1₁.12) Consider a random process X(t)= Acos(wt+Ⓒ) where A and are independent uniform random variables over the (-k, k) and (-7, 7) respectively. Find the mean, autocorrelation function, autocovariance function and variance of X(t). a.
Consider patients coming to a doctor's office at random point in time. Let X, denote the time (in hrs) that the nth patient has to wait before being admitted to see the doctor. Describe the random process X₁, n 21 A random process is defined by X(t)=T+(1-1) where T'is uniform random variable in (0, 1) Find the CDF of X(t) b. Find E(X(t)) and Cxx (1₁.12) Consider a random process X(t)= Acos(wt+Ⓒ) where A and are independent uniform random variables over the (-k, k) and (-7, 7) respectively. Find the mean, autocorrelation function, autocovariance function and variance of X(t). a.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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Tutorial Set 2
1. Consider patients coming to a doctor's office at random point in time. Let X, denote the
time (in hrs) that the nth patient has to wait before being admitted to see the doctor.
Describe the random process X₁, n≥1
2. A random process is defined by X(t)=T+(1-1) where T'is uniform random variable in
QUESTIONS ON RANDOM PROCESSES
a.
Find the CDF of X(t)
b. Find E(X(t)) and Cxx (1₁.1₂)
3. Consider a random process X(t)= Acos(wt+Ⓒ) where A and are independent
uniform random variables over the (-k, k) and (-7, 7) respectively. Find the mean,
autocorrelation function, autocovariance function and variance of X(t).
4. Consider a random process X(t)=Bcos(5t + D) where B and
variables. B is random variable with mean 0 and variance 1.
in [-7, 7]. Find the mean and autocovariance of the process.
5. Suppose X() is a random process with mean 3 and autocorrelation of
are independent random
is uniformly distributed
Rxx (1₁,1₂)=9+4e-²-¹. Determine the mean, variance and covariance of the random
variable Z = X(5) and W = X(8)
6. Let X(t)= Acost+Bsint where A and B are independently normally distributed
random variables N(0, ²). Find the covariance function of the X(t) process.
7. For the process X(t) given by X(t)= acost+bsint, where a and b are independent
random variables with E(a)=E(b)=0, var (a)= var (b)=o² and is constant. Obtain the
mean, variance and correlation of X(t) process.
8. Suppose X(t) is a random process with mean 2 and autocorrelation
Rxx (1₁,1₂)=5+3e-Determine the mean, variance and covariance of the random
variables Z = X(4) and W = X(6).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18da6a07-842d-45d7-986a-77f7658eca9f%2Fd1e1d0e9-2ead-4d35-afb0-f3ee1063b197%2F59hdx6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(0, 1)
Tutorial Set 2
1. Consider patients coming to a doctor's office at random point in time. Let X, denote the
time (in hrs) that the nth patient has to wait before being admitted to see the doctor.
Describe the random process X₁, n≥1
2. A random process is defined by X(t)=T+(1-1) where T'is uniform random variable in
QUESTIONS ON RANDOM PROCESSES
a.
Find the CDF of X(t)
b. Find E(X(t)) and Cxx (1₁.1₂)
3. Consider a random process X(t)= Acos(wt+Ⓒ) where A and are independent
uniform random variables over the (-k, k) and (-7, 7) respectively. Find the mean,
autocorrelation function, autocovariance function and variance of X(t).
4. Consider a random process X(t)=Bcos(5t + D) where B and
variables. B is random variable with mean 0 and variance 1.
in [-7, 7]. Find the mean and autocovariance of the process.
5. Suppose X() is a random process with mean 3 and autocorrelation of
are independent random
is uniformly distributed
Rxx (1₁,1₂)=9+4e-²-¹. Determine the mean, variance and covariance of the random
variable Z = X(5) and W = X(8)
6. Let X(t)= Acost+Bsint where A and B are independently normally distributed
random variables N(0, ²). Find the covariance function of the X(t) process.
7. For the process X(t) given by X(t)= acost+bsint, where a and b are independent
random variables with E(a)=E(b)=0, var (a)= var (b)=o² and is constant. Obtain the
mean, variance and correlation of X(t) process.
8. Suppose X(t) is a random process with mean 2 and autocorrelation
Rxx (1₁,1₂)=5+3e-Determine the mean, variance and covariance of the random
variables Z = X(4) and W = X(6).
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