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Let X have an exponential distribution with parameter λ. a. Determine E[X] and E[X^2] using partial integration.

Okay so I thought I could just plug that in my ti-89 or nspire cas cx, but neither can do it.

E[X] = $$\int_0^∞ xλe^{-λx} \,dx,$$ However that just gives me undef for both calculators. Wolfram alpha is happy to do it.

https://www.wolframalpha.com/input/?i=integral(xae%5E(-a*x))+from+0+to+infinity

Is there a way to do this on these calculators?

user45468
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  • You can solve this integral by hand using integration by parts, as shown here https://en.m.wikibooks.org/wiki/Statistics/Distributions/Exponential. As to why the Texas Instruments couldn't solve them that is interesting. Are you inputting everything in correctly? – WaveX Mar 11 '17 at 02:00
  • Yeah, I tried just using the letter a, and lambda – user45468 Mar 11 '17 at 02:03
  • https://cdn.discordapp.com/attachments/237426530806923264/289936334016086016/unknown.png if that shows up is the input – user45468 Mar 11 '17 at 02:03
  • The variable for the parameter shouldn't cause any issues, unless there is a value stored in there for a and/or $\lambda$. I've seen TI just do things in a weird way before too, like not simplifying an expression the whole way. – WaveX Mar 11 '17 at 02:08
  • The integral is convergence if and only if $\lambda>0$. Maybe that's the reason why $e^{a\cdot infinity}$ cannot be evaluated. I don't know how TI are programmed but, for example, Maple sometimes give weird results when it does not if the sign of a parameter, or if it is real or complex... – Taladris Mar 11 '17 at 12:44

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