Define a random variable X to be stochastically greater than a random variable Y if FX(t)...
Problem 4 Let X be a discrete random variable with probability mass function fx(x), and let t be a function. Define Y = t(X): that is, Y is the randon variable obtained by applying the function t to the value of X Transforming a random variable in this way is frequently done in statistics. In what follows, let R(X) denote the possible values of X and let R(Y) denote the possible values of To compute E[Y], we could irst find...
Let X be a random variable with PDF fx(X). Let Y be a random variable where Y=2|X|. Find the PDF of Y, fy(y) if X is uniformly distributed in the interval [−1, 2]
Let X be an exponential random variable with parameter A > 0, and let Y be a discrete random variable that takes the values 1 and -1 according to the result of a toss of a fair coin Compute the CDF and the PDF of Z = XY
Let X be an exponential random variable with parameter A > 0, and let Y be a discrete random variable that takes the values 1 and -1 according to the result of...
1. Let (X,Y) be a random vector with joint pdf fx,y(x,y) = 11–1/2,1/2)2 (x,y). Compute fx(x) and fy(y). Are X, Y independent? 2. Let B {(x,y) : x2 + y2 < 1} denote the unit disk centered at the origin in R2. Let (X',Y') be a random vector with joint pdf fx',y(x', y') = 1-'13(x',y'). Compute fx(x') and fy(y'). Are X', Y' independent?
A random variable Y is a function of random variable X, where y=x^3 and fx(x)=1 from 0 to 1 and =0 elsewhere. Determine fy(y). Ans: fy(y)=(1/3)y^(-2/3) for 0<y<1
7. Let X be a random variable with distribution function Fx. Let a < b. Consider the following 'truncated' random variable Y: if X < a, if X > b. (a) Find the distribution function of Y in terms of Fx. (It will be a good additional exercise to sketch FY though you don't have to hand it in.) (b) Evaluate the limit lim FY (y) b-00
A fair coin is tossed twice. Let X and Y be random variables such that: -X = 1 if the first toss is heads, and X = 0 otherwise. -Y = 1 if both tosses are heads, and Y = 0 otherwise. Determine whether or not X and Y are independent. So far, I have determined the the joint probability distribution as follows: x = 0 x = 1 y = 0 2/4 1/4 y = 1 0 1/4
4. Suppose that X is a random variable such that P(X < 0) = 0. You toss a fair coin and if the head comes up, you define Y to be VX; if the tail comes up, you define Y to be - VX. a. Find the cumulative distribution function of Y in terms of the cumulative distribution function of X. (You will probably want to consider two cases, one for y<0 and the other for y> 0.) b. Now...
(5 pts) Consider a random variable X with pdf V o S 0.5eX fx(x) = { 0.5e-2 x < 0 x > 0. 0.5 e-> o ΔΙ Let S 4x2 x < 0 g(x) = { 22 x 20, V ΔΙ and let Y = g(X). Determine fy(y).
A coin is tossed twice. Let
the random variable X denote the number of tails that occur in the
two tosses. Find the P(X ≤ 1)
Question 2: A coin is tossed twice. Let the random variable X denote the number of tails that occur in the two tosses. Find the P(Xs 1) a. 0.250 b. 0.500 c. 0.750 d. 1.000 e. None of the above