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For each of the following functions fi(x), (i) verify that they are legitimate probability density functions...

For each of the following functions fi(x), (i) verify that they are legitimate probability density functions (pdfs), and (ii) find the corresponding cumulative distribution functions (cdfs) Fi(t), for all t ? R.

f1(x) = |x|, ? 1 ? x ? 1

f2(x) = 4xe ?2x , x > 0

f3(x) = 3e?3x , x > 0

f4(x) = 1 2? ? 4 ? x 2, ? 2 ? x ? 2.

Math   Statistics-And-Probability   
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Answer #1

The pdf is valid since and

The CDF is for ,

The CDF is for ,

Thus the CDF is

The pdf is valid since and

The CDF is

The pdf is valid since and

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