b) Pr(X<4)=0.666667
c) Pr(X<2|X<4)=0.50
Suppose X has the following Uniform distribution if 0<x<6 f(x)=\ & 0 otherwise a) Sketch the...
3. Let X has the following pdf: {. -1 <1 fx(a) otherwise 1. Find the pdf of U X2. 2. Find the pdf of W X
Suppose X is a continuous random variable having pdf (1+x, -1 < x < 0, f(x) = { 1 – x, 0 < x <1, lo, otherwise (a) Find E(X2). (b) Find Var(X2).
4. Two RVs with a joint pdf given as follows fx.x ), 0<x< 1,0 <y<1 otherwise (a) Find fr ). (6 point) (b) Find fxy(x[y). (6 points) (c) Are X and Y independent? (clearly show justification for credit) (6 points)
4. The joint distribution of X and Y is given by 0 otherwise (a) Are X and Y independent? Explairn. (b) Find the marginal probability function (pdf) of Y, fy (). (c) Provide the integral for finding P(X < Y), but DO NOT evaluate.
If X has a gamma distribution with alfa = 2 and beta = 1, find pl 1.6 < X <2.8) Goma Distidiosa Fox) = f(...) for x 30 Q2. Let X be a continuous random variable with f(x) = 0.5ež for x > 0 and 0 otherwise. Find the expected value of g(x) = ei x <2.8) for xxo Gumma. Distribution F() =fQ, XB) - Ba otherwise
Question-2 Consider the joint uniform density function C for 22 + y2 < 4, f(x,y) 0 otherwise. What is the value of c? 0 What is P(X<0)? What is P(X <0, Y <0)? What is f( x | y=1)?
Question No. 6 Suppose that the random variable X has the following uniform distribution: 2 f(x)= 3 ,other wise (18) P(0.33 < X < 0.5) = (A) 0.49 (B) 0.51 (C) 0 (D) 3 (19) P(X> 1.25) = (A) 0 (B) 1 (С) 0.5 (D) 0.33 (20) The variance of X is (A) 0.00926 (B) 0.333 (C) 9 (D) 0.6944
7. Suppose that the joint density of X and Y is given by f(x,y) = e-ney, if 0 < x < f(z, y) = otherwise. Find P(X > 1|Y = y)
(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)...
4. Suppose X has a discrete uniform distribution: the distribution function of X 5. A random variable Z has the pmf bclow. P (X-х,)-1 , is|2 n. Find 0 Pz(z) 0.20 0.16 0.4 a (1) What is thevalue of a ? (2) What is P(l S Z <3)? (3) What is Fz (1.7)? 6.