Problem 5 Three numbers (a, b, and c) are picked at random in the continuous range...
Problem 7: Let X and Y be two jointly continuous random variables with joint PDF 4 (x y) otherwise a) Find P(0< Y< 1/2 I x-2) b) For what value of A is it true that P(0 < Y < ½ |X> A)-5/16
1) Suppose that three random variables, X, Y, and Z have a continuous joint probability density function f(x, y. z) elsewhere a) Determine the value of the constant b) Find the marginal joint p. d. fof X and Y, namely f(x, y) (3 Points) c) Using part b), compute the conditional probability of Z given X and Y. That is, find f (Z I x y) d) Using the result from part c), compute P(Z<0.5 x - 3 Points) 2...
Problem 9: Suppose X is a continuous random variable, uniformly distributed between 2 and 14. a. Find P(X <5) b. Find P(3<X<10) c. Find P(X 2 9)
X with density fcx)3/56 ir 2<<4 5. Consider a continuous random variable X with density f(x)- otherwise a. Find P(1 <X<3) b. Find ECX)
Q2) (20 points) The joint pdf of a two continuous random variables is given as follows: < x < 2,0 < y<1 (cxy0 fxy(x, y) = } ( 0 otherwise 1) Find c. 2) Find the marginal PDFs of X and Y. Make sure to write the ranges. Are these random variables independent? 3) Find P(0 < X < 110 <Y < 1) 4) What is fxy(x\y). Make sure to write the range of X.
5. Y is a continuous random variable with pdf f(y) = (4 – y)/8, 0<y< 4. (a) Find E(Y). (b) Find E(Y2). (c) Find Var(Y).
b. Let X be a continuous random variable with probability density function f(x) = kx2 if – 1 < x < 2 ) otherwise Find k, and then find P(|X| > 1/2).
Example 46. Let X be a random variable with PDF liſa - 1), 1<a < 3; f(a) = { à(5 – a), 3 < x < 5; otherwise. Find the CDF of X. @ Bee Leng Lee 2020 (DO NOT DISTRIBUTE) Continuous Random Var Example 46 (cont'd). Find P(1.5 < X < 2.5) and P(X > 4).
Problem 5. The joint density of X and Y is given by e" (z+y) fx.-otherwise. İf 0 < x < oo, 0 < y < 00, Consider the random variable Z-; a) Find the cumulative distribution function of Z b) What is the probability density function of Z?
8), Let X and Y be continuous random variables with joint density function f(x,y)-4xy for 0 < x < y < 1 Otherwise What is the joint density of U and V Y