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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _computeFractionForSampleSize(sampleSizeLowerBound, total, withReplacement):
 """ Returns a sampling rate that guarantees a sample of size >= sampleSizeLowerBound 99.99% of the time. How the sampling rate is determined: Let p = num / total, where num is the sample size and total is the total number of data points in the RDD. We're trying to compute q > p such that - when sampling with replacement, we're drawing each data point with prob_i ~ Pois(q), where we want to guarantee Pr[s < num] < 0.0001 for s = sum(prob_i for i from 0 to total), i.e. the failure rate of not having a sufficiently large sample < 0.0001. Setting q = p + 5 * sqrt(p/total) is sufficient to guarantee 0.9999 success rate for num > 12, but we need a slightly larger q (9 empirically determined). - when sampling without replacement, we're drawing each data point with prob_i ~ Binomial(total, fraction) and our choice of q guarantees 1-delta, or 0.9999 success rate, where success rate is defined the same as in sampling with replacement. """

        fraction = float(sampleSizeLowerBound) / total
        if withReplacement:
            numStDev = 5
            if (sampleSizeLowerBound < 12):
                numStDev = 9
            return fraction + numStDev * sqrt(fraction / total)
        else:
            delta = 0.00005
            gamma = - log(delta) / total
            return min(1, fraction + gamma + sqrt(gamma * gamma + 2 * gamma * fraction))