The CDF of the random variable (x) is (Fₓ(x)=begincases1-e-α x², & x≥0 0, & otherwise endcases) where (α>0). Find: the mean; the median; the mode.
a) Mean = (1/2α), Median = (√ln 2/α), Mode = 0
b) Mean = (1/α), Median = (√ln 2/α), Mode = 0
c) Mean = (1/2α), Median = (√ln 2/2α), Mode = 0
d) Mean = (1/α), Median = (√ln 2/2α), Mode = 0