  The statistical properties of finite-time Lyapunov exponents at the Ulam
point of the logistic map are investigated. The exact analytical expression for
the autocorrelation function of one-step Lyapunov exponents is obtained,
allowing the calculation of the variance of exponents computed over time
intervals of length $n$. The variance anomalously decays as $1/n^2$. The
probability density of finite-time exponents noticeably deviates from the
Gaussian shape, decaying with exponential tails and presenting $2^{n-1}$ spikes
that narrow and accumulate close to the mean value with increasing $n$. The
asymptotic expression for this probability distribution function is derived. It
provides an adequate smooth approximation to describe numerical histograms
built for not too small $n$, where the finiteness of bin size trimmes the sharp
peaks.
