Question 1136713
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No.<br>
The integral from 0 to infinity of f(x) = 2^(-x) is 1/ln(2) which is about 1.4427.<br>
For f(x) to be a probability density function, the integral has to be equal to 1.<br>
Note f(x) = 2^(-x) could be a probability density function if it were defined only for positive integer values of x, instead of having a continuous domain of x>0:<br>
2^(-1)+2^(-2)+2^(-3)+... = 1/2 + 1/4 + 1/8 + ... = 1.