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Question 4 A continuous random variable X which represents the amount of sugar (in kg) used by a family per week, has the probability density function (x)-{06r + 18x-12 ; ishervise : otherwise (iv) Determine the mean and variance of X (v) Determine Var (4X?). Question 5 Consider the following probability distribution for X 30.3 10.2 0.2 0.1 (i) Find E(X). (ii) Find E(2x +4x). (ii) Determine the MGF of X (iv) Calculate Var (X) using MGF ofx Question 6 The temperature X (Celcius) at a randomly sclected point in a commercial refrigerator is a random variable with probability density function 0 otherwise Determine the MGF of X
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