Question 4 Discrete random variable X takes 2 possible values: -1 and 2. Another discrete random variable Y takes 2 possible values: 0 and 3. The 1st moment of random variables X and Y about the origin are 1.625 and 2.25, respectively. Let Z be a random variable that follows Bernoulli distribution with p=0.6. Assume all random variables are independent. (a) Find the probability distributions of X and Y, respectively. (b) Find Var (X) and Var(Y). (c) Find Var (2X-3Y+4). (d) Find P[ZX +(1-Z)Y1]. [6 marks] [6 marks] [4 marks] [4 marks] Question 4 Discrete random variable X takes 2 possible values: -1 and 2. Another discrete random variable Y takes 2 possible values: 0 and 3. The 1st moment of random variables X and Y about the origin are 1.625 and 2.25, respectively. Let Z be a random variable that follows Bernoulli distribution with p=0.6. Assume all random variables are independent. (a) Find the probability distributions of X and Y, respectively. (b) Find Var (X) and Var(Y). (c) Find Var (2X-3Y+4). (d) Find P[ZX +(1-Z)Y1]. [6 marks] [6 marks] [4 marks] [4 marks] Question 4 Discrete random variable X takes 2 possible values: -1 and 2. Another discrete random variable Y takes 2 possible values: 0 and 3. The 1st moment of random variables X and Y about the origin are 1.625 and 2.25, respectively. Let Z be a random variable that follows Bernoulli distribution with p=0.6. Assume all random variables are independent. (a) Find the probability distributions of X and Y, respectively. (b) Find Var (X) and Var(Y). (c) Find Var (2X-3Y+4). (d) Find P[ZX +(1-Z)Y1]. [6 marks] [6 marks] [4 marks] [4 marks] Question 4 Discrete random variable X takes 2 possible values: -1 and 2. Another discrete random variable Y takes 2 possible values: 0 and 3. The 1st moment of random variables X and Y about the origin are 1.625 and 2.25, respectively. Let Z be a random variable that follows Bernoulli distribution with p=0.6. Assume all random variables are independent. (a) Find the probability distributions of X and Y, respectively. (b) Find Var (X) and Var(Y). (c) Find Var (2X-3Y+4). (d) Find P[ZX +(1-Z)Y1]. [6 marks] [6 marks] [4 marks] [4 marks] Question 4 Discrete random variable X takes 2 possible values: -1 and 2. Another discrete random variable Y takes 2 possible values: 0 and 3. The 1st moment of random variables X and Y about the origin are 1.625 and 2.25, respectively. Let Z be a random variable that follows Bernoulli distribution with p=0.6. Assume all random variables are independent. (a) Find the probability distributions of X and Y, respectively. (b) Find Var (X) and Var(Y). (c) Find Var (2X-3Y+4). (d) Find P[ZX +(1-Z)Y1]. [6 marks] [6 marks] [4 marks] [4 marks]