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To improve the forecasting capability of impactful solar energetic particle (SEP) events, the relation between coronal mass ejections (CMEs) and SEP events needs to be better understood. Here we present a statistical study of SEP occurrences and timescales with respect to the CME source locations and speeds, considering all 257 fast ($v_{CME}$ $\ge$ 900 km/s) and wide (angular width $\ge$ 60$^{\circ}$) CMEs that occurred between December 2006 and October 2017. We associate them with SEP events at energies above 10 MeV. Examination of the source region of each CME reveals that CMEs more often accompany a SEP event if they originate from the longitude of E20-W100 relative to the observer. However, a SEP event could still be absent if the CME is $<$ 2000 km/s. For the associated CME-SEP pairs, we compute three timescales for each of the SEP events, following Kahler (2005, 2013); namely the timescale of the onset (TO), the rise time (TR), and the duration (TD). They are correlated with the longitude of the CME source region relative to the footpoint of the Parker spiral ($ΔΦ$) and $v_{CME}$. The TO tends to be short for $|ΔΦ|$ $<$ 60$^{\circ}$ . This trend is weaker for TR and TD. The SEP timescales are only weakly correlated with $v_{CME}$. Positive correlations of both TR and TD with $v_{CME}$ are seen in poorly connected (large $|ΔΦ|$) events. Additionally, TO appears to be negatively correlated with $v_{CME}$ for events with small $|ΔΦ|$.