Statistics

1. Let X and Y be two continuous random variables having the joint probability density f(x,y)=4xy for 0<1, 0<1.
Find the joint probability density of Z=X^2 and W=XY

2. If X is the number of 7's obtained when rolling a pair of dice three times, find the probability that Y=X^2 will exceed 2.

3. If X is the total we roll with a pair of dice,for which the probability distribution is given below here, find the probability distribution of the remainder we get when the values of X are divided by 3

Element of sample space Probability X HHHH 1/16 4 HHHT 1/16 3 HHTH 1/16 3 HTHH 1/16 3 THHH 1/16 3 HHTT 1/16 2 HTHT 1/16 2 HTTH 1/16 2 THHT 1/16 2 THTH 1/16 2 TTHH 1/16 2 HTTT 1/16 1 THTT 1/16 1 TTHT 1/16 1 TTTH 1/16 1 TTTT 1/16 0