(a). Roll a die until you get your 17th ace. Let T be the number of...

(a). Roll a die until you get your 17th ace. Let T be the number of rolls you need to get that 17th ace.

Find E(T) and var(T).

(b). Let Y = T-17 = "number of non-aces rolled to get your 17th ace". Y is called a "negative binomial" random variable, with parameters r=17 and p= 1/6.

Find E(Y) and var(Y).

(c). Find the approximate value of P{ T > 120 }

This variance can also be found in a tedious way (but not requiring any cleverness) using the "moment-generating function" of X given by m(t) = E[ e^(tX)]. Look it up if you have OCD.

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Expert Solution

milcah answered 8 months ago

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