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- Let X and Y be random variables. Suppose Var(X) = 1.6, Var(Y) = 1.2, and Cov(X, Y) = 0.6. Let Z = -1.2X + 1.9Y + 4.2. Calculate Var(Z).Suppose we choose arbitrarily a point from the square with corners at(2,1), (3,1), (2,2), and (3,2). The random variable A is the area of the trianglewith its corners at (2,1), (3,1), and the chosen point. Compute E[A].A research center claims that that 31% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 1200 adults in that country, 33% say that would travel into space on a commercial flight if they could afford it. At alpa= 0.05, isthere enough evidence to reject the research centers claim complete parts a through d below
- Consider a biased random walk on the set { 1, 2, 3, 4} withprobability p = .2 of moving to the left. What is the probability of moving from 2 to 3 in exactly 3 steps if the walk hasa. reflecting boundaries? b. absorbing boundaries?If Y is a random variable, prove that it only takes positive integers.