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Question 1: Probability of Dealing Cords (10 marks) Consider cards dealt from a deck of 52 eardsl. Find the probability that a ran- domly dealt six-card hand consists of three of a kind and three of another kind. An example consists of three 10's and three 5's. Question 2: Roll 41 Die and Toss o Coin (.20 marks) Roll a fair dice and toss a coin. Let X and Y be discrete random variables, with X representing the number shown on the die; and Y = 1 if the coin lands on head and Y =0 ifit lands on tail. Let Z =X+Y; for example, ifthe dieroll is l andeoin lands on head. then Z(I.H)= 1+1 = 2. (i) Write the sample space of the random variable Z. (2 marks) (ii) Create a table for the probability mass function p(:r) of Z. (5 marks) (iii) Find the cumulative distribution function, F[z}. for Z and plot it {inst the values of :5. mm m e\\emen{ marks) e var' . (5 marks) (iv) C marks} {v) Ca