1. Suppose that the p.d.f. of a random variable X is as follows: for 0<x<2, for...
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.
5. Suppose that the probability distribution function (p.d.f.) of a random variable X is as follows: a-x3) for 0<x<1 o/w Sketch this p.d.f. and determine the values of the following probabilities: f(x) =
(50 points) Suppose that the joint p.d.f. of X and Y is as follows: for x 2 0, y 2 0, and x + y <1 elsewhere 2. 24xy f(x)0 a) Determine the value of P(X < Y). b) Determine the marginal p.d.f.'s for Xand Y c) Find P(X> 0.5) d) Determine the conditional p.d.f. of X|Y = 0.5 e) Find P(X> 0.5|Y 0.5) f) Find P(X> 0.5|Y> 0.5) g) Find Cov (X, Y)
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).
(1) Suppose the pdf of a random variable X is 0, otherwise. (a) Find P(2 < X < 3). (b) Find P(X < 1). (e) Find t such that P(X <t) = (d) After the value of X has been observed, let y be the integer closest to X. Find the PMF of the random variable y U (2) Suppose for constants n E R and c > 0, we have the function cr" ifa > 1 0, otherwise (a)...
2. Suppose that the p.d.f. of a random variable X is given as in last question. Now let Y 4-X3 Find its p.d.f
The random variable X has the following p.d.f. tx -9 - <I< an f(3) = 21 0, otherwise Use the moment generating function technique to determine the p.d.f. of Y=X? Hence or otherwise state the mean and variance of the random variable Y. (6 Marks)
1. Consider a continuous random variable X with the probability density function Sx(x) = 3<x<7, zero elsewhere. a) Find the value of C that makes fx(x) a valid probability density function. b) Find the cumulative distribution function of X, Fx(x). "Hint”: To double-check your answer: should be Fx(3)=0, Fx(7)=1. 1. con (continued) Consider Y=g(x)- 20 100 X 2 + Find the support (the range of possible values) of the probability distribution of Y. d) Use part (b) and the c.d.f....
The distribution function of a random variable X is given by 0 Fw={ F(2) = 1+2 <-1 -1<r<1 => 1 "iszai (a) (5 points) Find the p.d.f(f(x)) of X (b) (5 points) Find P(0.3 < X <0.5)
Let random variable x be a continiuos random variable and it's p.d.f is given as f(x)=3x^2, 0<x<1 Find the probobility that random variable X exceeds the value of 1/2