Suppose a random variable X has the following density function:
f(x) = { x , 0 ≤ x < 4,
0, o.w.
Let Y = 1 − sqrt(2−X2)/2. Find the density function for Y .
Suppose a random variable X has the following density function: f(x) = { x , 0...
PROBLEM 4 Let X be a continuous random variable with the following PDF 6x(1 - 1) if 0 <r<1 fx(x) = o.w. Suppose that we know Y X = ~ Geometric(2). Find the posterior density of X given Y = 2, i.e., fxy (2/2).
Suppose X is a random variable that has density function f(x) = (1/2)e^−|x| for −∞ < x < ∞. Find: (a) (2 pts) P(X < 10). (b) (4 pts) The c.d.f. of X2. (c) (4 pts) V ar(X)
Let X be a continuous random variable with the following probability density function f 0 < x < 1 otherwise 0 Let Y = 10 X: (give answer to two places past decimal) 1. Find the median (50th percentile) of Y. Submit an answer Tries 0/99 2. Compute p (Y' <1). Submit an answer Tries 0/99 3. Compute E (X). 0.60 Submit an answer Answer Submitted: Your final submission will be graded after the due date. Tries 1/99 Previous attempts...
Let X be a random variable with density function given by f(x) ={ 3 2x2, −1 ≤ x ≤ 1; 0, otherwise Find the density function Y = X2.
Suppose the random variable X has probability density function (pdf) - { -1 < x<1 otherwise C fx (x) C0 : where c is a constant. (a) Show that c = 1/7; (b) Graph fx (х); (c) Given that all of the moments exist, why are all the odd moments of X zero? (d) What is the median of the distribution of X? (e) Find E (X2) and hence var X; (f) Let X1, fx (x) What is the limiting...
4. Let X be a continuous random variable with probability density function: x<1 0, if if| if x>4 f(x) = (x2 + 1), 4 x 24 0 Find the standard deviation of random variable X.
2. Suppose a certain random variable Y has the following probability density function: f(y)-0. 125y for 0< y < 4 (a) If a random sample of 40 observations is selected from this distribution, sketch the approximate probability distribution of - 10 where x is the sample mean. (4 pts) b) What is the mean and variance of x? (2 pts) (c) How large would the sample have to be in order for x to have a standard deviation of 0.01?...
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Let X be a random variable with probability density function fx(2, -1 <z<3, 0 otherwise. Find the probability distribution of Y-X2 for 0 < y < 1, 1 < y < 9, and y > 9. [Obviously, fy(y)-0 for y < 0.1 Case 1: O < y < 1. Enter a formula below. Use * for multiplication, / for divison, ^ for power and sqrt for square root. For example, sqrt y...
Assume that X is a continuous random variable with the following probability density function. f(x)=3x2 for 0<x<1 Find the probability density function of Y=X2
4. Suppose two random variables X and Y has the following joint density function Cry, 22 Sy<1, f(x,y) = { 0, otherwise. (a) Find the constant C. (b) Find E(Y|X = 1/2). 5. Suppose X1, X2, ..., are i.i.d. random variables coming from the N(0,0%) population. (a) Determine the mean and variance for X. (b) Show that va bos (x2) – 1o60*) $ (0.2).