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.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
Solution to Q8
![(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).](/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).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON