Find CDF for random variable X where f(x)= x from 0<x<1 and f(x)= 2-x from 1<x<2. (SAME function)
Find CDF for random variable X where f(x)= x from 0<x<1 and f(x)= 2-x from 1<x<2....
2. For a discrete random variable X, with CDF F(X), it is possible to show that P(a < X S b)-F(b) - F(a), for a 3 b. This is a useful fact for finding the probabil- ity that a random variable falls within a certain range. In particular, let X be a random variable with pmf p( 2 tor c-1,2 a. Find the CDF of X b. Find P(X X 5). c. Find P(X> 4). 3. Let X be a...
(a) Let X be a continuous random variable with the cdf F(x) and pdf f(.1). Find the cdf and pdf of |X|. (b) Let Z ~ N(0,1), find the cdf and pdf of |Z| (express the cdf using ” (-), the cdf of Z; give the explicit formula for the pdf).
Let X be a random variable with CDF z<0 G()=/2 0 <IS2 z>2 1 Suppose Y = X2 is another random variable, find (a) P(1/2 X 3/2), (b) P(1s X< 2) (c) P(Y X) (d) P(X 2Y). (f) If Z VX, find the CDF of Z. (d) P(X+Y 3/4)
The CDF of a random variable X is given by: F(x) = 1 - e-2x for x >= 0 0 for x < 0 a) Find the PDF of X. b) Find P(X > 2) c) P(-3 < X ≤ 4)
2. A random variable X has a cdf given by F(x) = 1 . x < 0 0 < x < 1 <3 x > 3 11, (f) What is P(X = 1)? (g) Find E(X), the expectation of X. (h) Find the 75th percentile of the distribution. Namely, find the value of 70.75 SO that P(X < 70.75) = F(710.75) = 0.75. (i) Find the conditional probability P(X > X|X > 3).
The random variable X has CDF 0 <-1, Ex(x) = 0.2 -1 < 0, 0.7 0 x<1, 1 21. (a) Draw a graph of the CDF (b) Write Px(), the PMF of X. Be sure to write the value of Px(a) for all r from-oo to oo. Given the random variable X in problem ii), let V g X)X. (a) Find P(v). (b) Find Fy(v). (c) Find EIV]
1. Suppose that X is continuous random variable with PDF f(x) and CDF F(x). (a) Prove that if f(x) > 0 only on a single (possible infinite) interval of the real numbers then F(x) is a strictly increasing function of x over that interval. [Hint: Try proof by contradiction]. (b) Under the conditions described in part (a), find and identify the distribution of Y = F(x). 2. Suppose now that X ~ Uniform(0, 1). For each of the distributions listed...
(a) Below is the CDF for a discrete random variable, X if x 1 1/2 if 1 x< 2 if 2 x 3 7/8 if 3 x 4 F(x) = 3/4 2 1 if nx <n+1. Describe the probability 2n In general, note that for any positive integer n, F(x) distribution of X by finding P(X 1), P(X = 2), P(X positive integer n, and describe an experiment that would result in this random variable X. 3), and the general...
Suppose that X is a random variable whose cumulative distribution function (cdf) is given by: F(x) = Cx -x^2, 0<x<1 for some constant C a. What is the value of C? b. Find P(1/3 < X < 2/3) c. Find the median of X. d. What is the expected value of X?
For a random variable X with cumulative distribution function (cdf) Fx(x) = 1- (2/x)^2 ,x>2. (a).Find the pdf fX(x). (b).Consider the random variable Y = X^2. Find the pdf of Y, fY (y).