After shuffling a deck of 52 cards, a dealer deals out 5. Let X = the number of suits represented in the five-card hand. a.?? how that the pmf of ?X i? s [Hint: p(1) = 4P( all are spades),p(2) =6P( only spades and hearts with at least one of each suit), and p(4) = 4P(2 spades ? one of each other suit). b.Compute ?, ?2 , and ?.

Answer: Step1: After shuffling a deck of 52 cards, a dealer deals out 5. Where, n = 52, x = 5. Let x = the number of suits represented in the five - card hand. Total number of hands is N = c = 2598960. 5 Step2: a). Given, x 1 2 3 4 p(x) 0.002 0.146 0.588 0.264 The pmf of ‘x’ is P(X = x) = Step3: 2 b). To compute , , and . Mean = E(x) = xp (x) = 1(0.002) + 2(0.146) + 3(0.588) +4(0.264) E(x) = 3.114. var(x) = = E[x E(x) ] 2 2 = (x E(x) ) p(x) = (1- (3.114) ) *.002 + (2 (3.114) ) 0.*46 + (3 (3.114) ) 0.5*8 2 + (4 (3.114) )*0.264 2 = 6.5830. Standard deviation = = var(x) = 6.5830 = 2.5657 Therefore, E(x) = 3.114, = 6.5830, = 2.5657.