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- X and Y are independent random variables with variances 2 and 3.Find the variance 3X+4Y.In a large lot of manufactured items, 10% contain exactly one defect and 5% contain more than one defect. If ten items are randomly selected from this lot for sale, the repair cost total Y1 +3Y2, where Y1 denote the number among the ten having one defective and let Y2 denote the number with two or more defects. Find the expected value and variance of the repair cost. Assume that Cov(Y1, Y2) =-0.05.Let A be a random variable with an expected value of E(X) = 32 and a variance Var(X) = 38. Find the expected value and variance of the following linear combinations: a) E(A+7)= , Var(A+7) =
- Let X1 be a normal random variable with mean 2 and variance 3 and let X2 be a normal random variable with mean 1 and variance 4. Assume that X1 and X2 are independent. (a) What is the distribution of the linear combination Y = 2X1 + 3X2? (b) What is the distribution of the linear combination Y = X1 – X2?Company A claims that the variance of the life of its appliances is less than the variance of the life of company B's appliances. A random sample of the lives of 22 of company A's appliances has a variance of 3.3. A random sample of the lives of 21 of company B's appliances has a variance of 4.9. At α=0.01, can you support company A's claim? Complete parts (a) through (e).The profit for a new product is given by Z=3X- Y-5 . If X and Y are independent random variables with Ox=1 and Oy=V2. What is the variance of Z ?
- Let X1 be a normal random variable with mean 2 and variance 3 and let X2 be a normal random variable with mean 1 and variance 4. Assume that X1 and X2 are independent. (a) What is the distribution of the linear combination Y = 2X1 +3X,? (b) What is the distribution of the linear combination Y = X, – X,?Suppose that a random man's weight from a certain population is M~ Normal (μ = 200, o²49) and a random woman's weight is W ~ Normal( 140, o² = 25). If M and W are independent, what is the variance of the difference between a man's weight and a woman's weight, i.e. Var (M-W)? (a) 340 (b) 24 (c) 140 (d) 200 (e) None of the aboveSuppose the variance of the difference of two random variables X and Y is zero. Then, show that X = Y + c for some constant c almost surely. Also find the value of c.
