Is normal for 4 year old to have a fast heart beat while sleeping?

Depends: Depends on how fast the heart rate is. Normal heart rate for most 4 year olds is between 80 and 120 bpm. See link below: http://www.Nlm.Nih.Gov/medlineplus/ency/article/003399.Htm.

Depends: Will depend on the heart rate. A child's resting heart rate is faster than that of an adult. During sleep, heart rates do change. Rem sleep (rapid eye movement) can increase heart rates to over 20% of resting rates. An abnormally fast heart rate in a child is typically over 220/min.