2.2 0 otherwise Find out the p.d.f. of Y - In(X) 2.3 Continue on above, find...
1. Let the joint p.d.f of X and Y be 2xe if 0 < x < 1 and y > x2 fxy(z, y) 0, otherwise. (a) Find the marginal p.d.f.'s of X and Y, respectively (b) Compute P(Y < 2X2) 1. Let the joint p.d.f of X and Y be 2xe if 0
Below is the p.d.f for the random variables X and Y, f(x,y)-36 0 otherwise Find the following probability Pr(x> 2) O 7/9 2/3 O 8/9
Find the conditional p.d.f.’s f(y|x) and f(z|x, y). 4. Suppose that random variables (X, Y, Z) have the joint p.d.f. f(x,y,z)-' 0, otherwise . ind the conditional p.d.f.'s f(yx) and f (z x,y
The joint p.d.f of \(X\) and \(Y\) is given by$$ f(x, y)=\left\{\begin{array}{ll} c(1-y), & 0 \leq x \leq y \leq 1 \\ 0 & \text { otherwise. } \end{array}\right. $$Determine the value of \(c\). Find the marginal density of \(X\) and the marginal density of \(Y\) Find the conditional density of \(X\) given \(Y\). Are \(X\) and \(Y\) independent? Why? Find \(E(X-2 Y)\).
Let, f(x)= 1/15e-x/15, 0≤ x < ∞ be the p.d.f. of X i. find the c.d.f., F(x), for f(x). ii. find the values of µ and ?2. iii. what is the moment generating function? iv. what is the probability that 20<x<40? v. what percentile is µ? vi. what is the value of the 25th percentile?
Let X and Y be random variables for which the joint p.d.f. is as follows: f (x, y) = 2(x + y) for 0 ≤ x ≤ y ≤ 1, 0 otherwise.Find the cumulative distribution function (c.d.f.) of X and Y.Find p.d.f. of Z=X+Y.
1. Suppose that the p.d.f. of a random variable X is as follows: for 0<x<2, for 0 〈 x 〈 2. r for 0<< f(x) = 0 otherwise. Let Y - X (2 - X). First determine the c.d.f. of Y, then find its p.d.f. (Hint: when computing c.d.f., plotting the function Y- X(2 - X) which may help. )
Find Var(2X-Y) Two random variables X and Y are i.i.d. and their common p.d.f. is given by f )- c(1+r) if 0 <r < 1. otherwise. f(3) = 10
Let X have the p.d.f. f(x) = 3(1−x)2 for 0 < x < 1. Find p.d.f. of Y = (1−X)3.
QUESTION 12 Let the random variable X and Y have the joint p.d.f. f(x,y) =(zy for 0< <2, 0 < y <2, and z<y otherwise Find P(0KY <1) 16 QUESTION 13 R eter to question 12. Find P(o < x <3I Y-1).