X is a Normally distributed random variable with a mean of 10 and a variance of25 (or more succinctly,XN(10,25)). SupposeYis another random variable andsuppose its value is determined in the following way:You take a draw of the random variableX. IfX >20, then you will flip a faircoin andYwill take on the value 4 if a head is obtained and the value 3 if a tail isobtained. If on the other handX <20, then you will instead roll a fair six-sideddie, and the value ofYwill be equal to the value showing on the die.

(a) Find the probability distribution ofY.

(b) Find the probability distribution ofYifX= 2.

(c) Find the probability distribution ofYifX= 50.

(d) AreXandYindependent? Explain.