Generate a random date between two other dates

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Convert both strings to timestamps (in your chosen resolution, e.g. milliseconds, seconds, hours, days, whatever), subtract the earlier from the later, multiply your random number (assuming it is distributed in the range [0, 1]) with that difference, and add again to the earlier one. Convert the timestamp back to date string and you have a random time in that range.

Python example (output is almost in the format you specified, other than 0 padding – blame the American time format conventions):

import random
import time
    
def str_time_prop(start, end, time_format, prop):
    """Get a time at a proportion of a range of two formatted times.

    start and end should be strings specifying times formatted in the
    given format (strftime-style), giving an interval [start, end].
    prop specifies how a proportion of the interval to be taken after
    start.  The returned time will be in the specified format.
    """

    stime = time.mktime(time.strptime(start, time_format))
    etime = time.mktime(time.strptime(end, time_format))

    ptime = stime + prop * (etime - stime)

    return time.strftime(time_format, time.localtime(ptime))


def random_date(start, end, prop):
    return str_time_prop(start, end, '%m/%d/%Y %I:%M %p', prop)
    
print(random_date("1/1/2008 1:30 PM", "1/1/2009 4:50 AM", random.random()))

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