SB550: QUIZ I May 31, 2016 1. (15 points)The life expectancy (in days) of electronic components has density function given by: f (x) = ax2 + 2ax + (a) (5 points) Solve for a (b) (5 points) Find the expected value of X (c) (5 points) solve for P (2 < x < 4)? 1 a 2 f or 0 < x < 4. 2. (20 points) A discrete random variable has the PMF shown in Table 2. Table 3 provides the joint probability of X and Y , where X represents a person's poverty status (above or below the poverty line) and Y represents a person's racial status. Table 2: Poverty in the United States X Below poverty Above poverty Y (White) (Black) Hispanic 0.15 0.18 0.21 0.20 0.14 0.12 (a) (5 points) Find the marginal distributions. (b) (5 points) Find P r(Above poverty|Hispanic) (c) (5 points) Eddie claims that race and poverty status are mutually exclusive. Gillham disagrees. Who's correct? Mathematically explain. (d) (5 points) Weidtman says that race and poverty status are rather independent. Compeau 2 wants proof. Please explain mathematically whether race and poverty status are indepoendent. 3. (5 points) The following table gives the joint PMF of random variables X and Y , where X =the first year rate of return (%) expected from investment A, and Y = first year rate of return (%) expected from investment B. Table 3. X(%) Y(%) -10 0 20 30 50 20 0.27 0.00 0.08 0.04 0.16 0.10 0.00 0.35 Find f (Y = 20|X = 20) 4. (10 points) A discrete r.v. X has the PMF shown in Table 2. Table 2. X f (X) 5 7 8 10 b 8b 2b 17b (a) (6 points) For this to be a true PMF, what must the value of b be? Show your work 3 (b) (4 points) Find P (7 < X < 10) 4