Show me the detail how did you find the answer.
Show me the detail how did you find the answer. X, Y, and Z are independent...
2. If X and Y are independent random variables, X has a normal distribution with mean 2 variance 4, and Y has a chi-square distribution with 9 degrees of freedom, then find u such that P(X > 2+11,7)=0.01.
Let X, Y be two independent exponential random variables with means 1 and 3, respectively. Find P(X> Y)
Suppose X and Y are independent random variables with Exponential(2) distribution (Section 6.3). We say X ~ Exponential(2) if its pdf is f(x) = -1/2 for x > 0.
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;
4.3. Let X and Y be independent random variables uniformly distributed over the interval [θ-, θ + ] for some fixed θ. Show that W X-Y has a distribution that is independent of θ with density function for lwl > 1.
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.
1. Let Xi,X2,... .X, be independent identically distributed N( 5,4 ran dom variables Find (use tables or software) t such that (a) P(X-51 > t) = .95 1-2-) >t) = .05 (c) P0% (X (d) P(LL52 *)2 > t) > t) .95 .95 where 82- Σ(x,-x)2
Random variables z and y described by the PDF if x-+ yo 1 and x.> 0 and y, > 0 0 otherwise a Are x and y independent random variables? b Are they conditionally independent given max(x,y) S 0.5? c Determine the expected value of random variabler, defined byr xy.
Let f(x, y) 2e-(x+y), x > 0, y > 0. Show that X, Y are independent. What are the marginal PDFS of each?
Can someone help me with this? Show that two jointly normally
distributed random variables are independent if they are
uncorrelated?
Additional Info:
Thank's a lot!!!
Let (*) ~ ~[(*) (*)) with oš> 0, 0} > 0. NX Then YlX^N (wy +O20yx(– Hx), oz, – 022Oxy@yx). That is, the regression function is here linear (in X): E[Y|X] = E[Y]+B(X – E[X]) = Hy +B(X – Hx), where B = Cov(X, Y) = pºy; recall: =vx= POD Cov(X, Y) = Oxy =...