Assume that X and Y are independent and follow normal distributions with Hx (a) evaluate P(X...
6. Assume that X and Y are independent and follow normal distributions with px (a) evaluate P(X + Y 〉 24) (2pt) (b) find x such that P(x 〈 X-Y 〈 10) 20, σ = 4 and μγ-10, σ = 2. 0.2 (3pt)
4. Let X, Y, and Z be independent random variables, each with the standard normal distribution. Compute the following: (a) P[X + Y> Z +2 (b) Var3x 4Y;
Let X, Y be two independent exponential random variables with means 1 and 3, respectively. Find P(X> Y)
Problem 8. Suppose that XGeom(p) and Y ~ Geom(r) are independent. Find the probability P(X <Y).
Let f(x, y) 2e-(x+y), x > 0, y > 0. Show that X, Y are independent. What are the marginal PDFS of each?
Let X, Y ~ 10,11 independently. Find P(max(X, Y} > 0.8 1 min(X, Y} = 0.5)
Question 12: Let X and Y have the joint probability density function Find P(X>Y), P(X Y <1), and P(X < 0.5)
Let f(x,y) = 12e-2(x+y), x > 0, y > 0. Show that X, Y are independent. What are the marginal PDFs of each?
Look at the image, thank you. For a standard normal distribution, find c if P(z>c) = 0.6906 c=
Problem 8: 10 points Suppose that (X, Y) are two independent identically distributed random variables with the density function defined as f (x) λ exp (-Ar) , for x > 0. For the ratio, z-y, find the cumulative distribution function and density function.