T has cumulative distribution function F(t) = 1-(2/t)?, t> 2 otherwise Let Y = T2 and...
Let Y be a continuous random variable with the following cumulative distribution function: for y <a 1-e-0.5(y-a)", for y>a where a is a constant. What is the 75th percentile of Y? F(y)= ŞO, Possible Answers [ A ]F(0.75) Ba-v2ln(4/3) ca+ √2ln(4/3) Da-2/in2 Ea+2 Vina
Exercise 1 Let X be a random variable that has moment generating function My(t) = 0.5-t2-t Find P[-1<x< 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)...
Exercise 3.37. Suppose random variable X has a cumulative distribution function F(x) = 1+r) 720 x < 0. (a) Find the probability density function of X. (b) Calculate P{2 < X <3}. (c) Calculate E[(1 + x){e-2X].
Define the cumulative distribution function F(t) oft by F(t) = P(W <t). Shade the region consisting of each point (x, y) in which x > 0, and F(X) < y < 1. Compute the area of the shaded region. Let X be binomial with parameters n = 10 and p = 0.5. Compute P(X = 5). Compute P(3 sX s 6). Compute P(X s 3). Submit You have used 0 of 3 attempts The annual income of graduates from college...
(15 points) Let X be a continuous random variable with cumulative distribution function F(x) = 0, r <α Inr, a< x <b 1, b< (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
Please answer both. . Suppose that Y is a random variable with distribution function below. 1-e-v/2, 0, y > 0; otherwise F(y) = (a) Find the probability density function (pdf) f(y) of Y. yso (b) E(Y) and Var(Y) 5. Suppose X is a random variable with E(X) 5 and Var(X)-2. What is E(X)?
Let X be a continuous random variable with cumulative distribution function F(x) = 1 − X−α x ≥ 1 where α > 0. Find the mean, variance and the rth moment of X. Question 1: Let X be a continuous random variable with cumulative distribution function where a >0. Find the mean, variance and the rth moment of X
Let X be a random variable with the following cumulative distribution function (CDF): y<0 (a) What's P(X < 2)? (b) What's P(X > 2)? c)What's P(0.5 X < 2.5)? (d) What's P(X 1)? (e) Let q be a number such that F(0.6. What's q?
2. Let X be a continuous random variable with pdf ( cx?, [xl < 1, f(x) = { 10, otherwise, where the parameter c is constant (with respect to x). (a) Find the constant c. (b) Compute the cumulative distribution function F(x) of X. (c) Use F(x) (from b) to determine P(X > 1/2). (d) Find E(X) and V(X).