Sample Question #64 (probability theory)

If random variable *X *is normally distributed, is *X/k, *where *k *is a known constant, also normal? Why or why not? Please "prove" your answer using the pdf.

(Comment: this question is an example where just memorizing properties you learned in textbooks is not sufficient. You must understand the why’s in addition to the what’s – just like in science!)

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ANSWER

First you should realize that the question only makes sense if k is not 0. Whenever you see a division problem, always check whether the denominator can be 0.

Otherwise, the pdf just undergoes a scalar transformation, which means X/k is also a normal random variable.