Solution Found!
Suppose that we are to observe two independent random
Chapter 5, Problem 161SE(choose chapter or problem)
Suppose that we are to observe two independent random samples:\(Y_{1}, Y_{2} \ldots \ldots . Y_{n}\) denoting a random sample from a normal đistribution with mean \(\mu_{1}\) and variance \(\sigma_{1}^{2}\); and \(X_{1}, X_{2}, \ldots, X_{m}\) denoting a random sample from another normal distribution with mean \(\mu_{2}\) and variance \(\sigma_{2}^{2}\) An approximation for \(\mu_{1}-\mu_{2}\) is given by \(Y^{-}-X^{-}\), the difference between the sample means. Find \(E\left(Y^{-}-X^{-}\right)\) and \(V\left(Y^{-}-X^{-}\right)\).
Equation Transcription:
Text Transcription:
Y_1,Y_2........Y_n
mu1
sigma_1^2
X_1,X_2,...,X_m
sigma_2^2
mu_1-mu_2
Y^- - X^-
E(Y^- - X^-)
V(Y^- - X^-)
Questions & Answers
QUESTION:
Suppose that we are to observe two independent random samples:\(Y_{1}, Y_{2} \ldots \ldots . Y_{n}\) denoting a random sample from a normal đistribution with mean \(\mu_{1}\) and variance \(\sigma_{1}^{2}\); and \(X_{1}, X_{2}, \ldots, X_{m}\) denoting a random sample from another normal distribution with mean \(\mu_{2}\) and variance \(\sigma_{2}^{2}\) An approximation for \(\mu_{1}-\mu_{2}\) is given by \(Y^{-}-X^{-}\), the difference between the sample means. Find \(E\left(Y^{-}-X^{-}\right)\) and \(V\left(Y^{-}-X^{-}\right)\).
Equation Transcription:
Text Transcription:
Y_1,Y_2........Y_n
mu1
sigma_1^2
X_1,X_2,...,X_m
sigma_2^2
mu_1-mu_2
Y^- - X^-
E(Y^- - X^-)
V(Y^- - X^-)
ANSWER:
Answer:
Step 1 of 1:
Suppose that we are to observe two independent random samples: denote a random sample from a normal distribution with mean and variance and denoting a random sample from another normal distribution with mean and variance
An approximation for is given by , the difference between the sample means.
We need to find the value of
We can write as,
……(1)
The mean of a sample of measured responses is given by