Question
The random variable Z has a Normal distribution with mean 0 and variance 1. Show that...
The random variable Z has a Normal distribution with mean 0 and variance 1. Show that the expectation of Z given that a < Z < b is o(a) – °(6) 0(b) – (a)' where Ø denotes the cumulative distribution function for Z.
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A Since Z ē con le sue (pdf) Von * Sace, Z«N60,1); que * Elz/aczab] - Sex falt) de a na z <3 2:6 Z=0 Plzebb Pizzas - ; tona Let - t = azdz=dt -- $2 t e da = I to tebe the & dt = 1 lethat 2527 ta 2 a San t-a² 22b ito 2-0 U21 - Sete dz = -4,601 - BEZSbb - P{Zsar = $(6) - Play E[zlac Zab] = o(a) - $(6) q(6) - 9(a)
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