Question

code class="asciimath">Consider the exponential distribution f(t) = ((1)/(\tau ) )e -(t)/(\tau ) (f(t) = 0 for t < 0). (a) Prove that the parameter \tau is the mean value of t, i.e. \tau = t ̄. (b) Prove that \tau is also the standard deviation, \sigma t = \tau . (c) Find the probability that any one value would fall in the range t ̄\pm \sigma t.

Name: code classasciimathconsider the exponential distribution ft 1tau e ttau ft 0 for t 0 a prove that the parameter tau is the mean value of t ie tau t b prove that tau is also the standard devi 59204
Uploaded: 2023-01-12T17:09:05-08:00
Duration: 2 min 46 s
Channel: Sri K
Description: code classasciimathconsider the exponential distribution ft 1tau e ttau ft 0 for t 0 a prove that the parameter tau is the mean value of t ie tau t b prove that tau is also the standard devi 59204

          code class="asciimath">Consider the exponential distribution f(t) = ((1)/(\tau ) )e -(t)/(\tau ) (f(t) = 0 for t < 0). (a) Prove that the parameter \tau is the mean value of t, i.e. \tau = t ̄. (b) Prove that \tau is also the standard deviation, \sigma t = \tau . (c) Find the probability that any one value would fall in the range t ̄\pm \sigma t.

Added by Erica J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

01/12/2023

Step 1

\] --- (a) Prove that \(\tau\) is the mean value \(\bar{t}\). Show more…

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code class="asciimath">Consider the exponential distribution f(t) = ((1)/(\tau ) )e -(t)/(\tau ) (f(t) = 0 for t < 0). (a) Prove that the parameter \tau is the mean value of t, i.e. \tau = t ̄. (b) Prove that \tau is also the standard deviation, \sigma t = \tau . (c) Find the probability that any one value would fall in the range t ̄\pm \sigma t.