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A normally distributed random variable has density
Chapter 4, Problem 60E(choose chapter or problem)
A normally distributed random variable has density function
\(f(y)=\frac{1}{\sigma \sqrt{2 \pi}} e^{-(y-\mu)^{2} /\left(2 \sigma^{2}\right)}\), \(-\infty<y<\infty\).
Using the fundamental properties associated with any density function, argue that the parameter
\(\sigma\) must be such that \(\sigma>0\).
Equation Transcription:
Text Transcription:
f(y)=12e-(y-)2/(22)
-infinity<y<infinity
sigma
sigma>0
Questions & Answers
QUESTION:
A normally distributed random variable has density function
\(f(y)=\frac{1}{\sigma \sqrt{2 \pi}} e^{-(y-\mu)^{2} /\left(2 \sigma^{2}\right)}\), \(-\infty<y<\infty\).
Using the fundamental properties associated with any density function, argue that the parameter
\(\sigma\) must be such that \(\sigma>0\).
Equation Transcription:
Text Transcription:
f(y)=12e-(y-)2/(22)
-infinity<y<infinity
sigma
sigma>0
ANSWER:
Answer:
Step 1 of 1:
A normally distributed random variable has density function,
……(1)
Using the properties associated with density function, argue that the parameter must be such that
The properties of density function If is a density function for a continuous
random variable, then