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Question: please answer part d...

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Please answer part D

1. An important integral in probability theory ise dr. Since we do not have an ele- mentary antiderivative of e, we are unable to evaluate this integral directly. However, suppose that the improper integral converges such that where I is currently unknown but will be determined in Part (b) of this problem. (a) Show that where D(a) is the disk centered at the origin and with radius a. (b) Deduce that I VT by rewriting the improper integral from Part (a). Remember (c) Using the change of variable x = V2-t, show that (d) In probability and statistics, the normal distribution with mean u and standard to fully justify your answer. / e-r2/2 dz V2т. deviation σ has the shape of the function e (z mu),(2 2). Using the results of parts (a) through (c) and the change of variables x ơu+ , normalize this function, that is, find the constant this function should be multiplied by to make it a probability distribution

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