Problem 3. Probability Density Functions

Question

2 points possible (graded, results hidden)

For t∈R, define the following two functions:
f1(t)=1/√2πexp(−max(1,t^2)^2)


and
f2(t)=1/√2πexp(−min(1,t^2)^2).


In this problem, we explore whether these functions are valid probability density functions.

Determine whether the function f1 is a valid PDF for a continuous random variable that can take any value on the real line. If not, is there a number c>0, such that cf1 is a valid PDF?

Yes, it is a valid PDF.
No, it is not a valid PDF, but there is a constant c making cf1 a valid PDF.
No, it is not a valid PDF, and there is no constant c making cf1 a valid PDF.
None of the above.
unanswered

Determine whether the function f2 is a valid PDF for a continuous random variable that can take any value on the real line. If not, is there a number c>0, such that cf2 is a valid PDF?
Yes, it is a valid PDF.
No, it is not a valid PDF, but there is a constant c making cf a valid PDF.
No, it is not a valid PDF, and there is no constant c making cf2 a valid PDF.
None of the above.
unanswered

Answer 1

So, what is the main characteristic of a PDF?
Correct - the area under the curve is 1.

See
https://www.jiskha.com/questions/1798820/For-t-R-define-the-following-two-functions-f1-t-12-exp-max-1-t2-2