The given PDF is .
1) The condition for valid PDF is
The probability,
and
The probability that the person dies between 70 and 80 is higher.
2) The conditional probability,
3) is maximized when
4) The expected value of the distribution is
Suppose Y follows a distribution with density function: f(y)={101846(100–y)? if(0<y<100) otherwise (Note: for this question you...
Suppose X follows a distribution with density function: f(x)-10.7kz2 031 otherwise (Note: for this question you can enter your answer in decimals as well as fractions) 1. What must the value of k be so that f(x)is a probability density function? Submit Answer Tries 0/3 2. Find the probability P(0.40.8) Submit Answer Tries 0/3 . Find median of the distribution of X Submit Answer Tries 0/3 4. Find E(Xx) Submit Answer Tries 0/3 5. Find Var(x) Submit Answer Tries 0/3...
Let the joint probability density function for (X, Y) be f(x,y) s+y), x>0, y>0, 7r+yCT, 0 otherwise. a. Find the probability P(X< Y). Give your answer to 4 decimal places. 28 Submit Answer Tries 0/5 b. Find the marginal probability density function of X, fx(x). Enter a formula in the first box, and a number for the second and the third box corresponding to the range of x. Use * for multiplication, / for division and л for power. For...
Suppose a joint probability density function for two variables X and Y is given as follows: {24x0, if 0 < x < 1,0 < y < 1 f(x, y) = otherwise Please find the probability p (w > 1) =? 3
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...
WILL THUMBS UP IF DONE NEATLY AND CORRECTLY! 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...
Thank you! Q8 Consider two independent continuous random variables X and Y with probability density function given as follows: fx(x) 1/10, 0<x< 10 0 otherwise 0y 10 fro-6/10, (y) = Enter all answers as a fraction (e.g. 4/5) or integer. a. Create the joint pdf from the marginals: <<y<0 otherwise. Submit Answer Tries 0/15 b, Find E(X 1 Y 2) Submit Answer Tries 0/5 C. Find E(Y 1 X = 2) Submit Answer Tries 0/5 d. Find Cov(X, Y) Submit...
1. Consider two random variables X and Y with joint density function f(x, y)-(12xy(1-y) 0<x<1,0<p<1 otherwise 0 Find the probability density function for UXY2. (Choose a suitable dummy transformation V) 2. Suppose X and Y are two continuous random variables with joint density 0<x<I, 0 < y < 1 otherwise (a) Find the joint density of U X2 and V XY. Be sure to determine and sketch the support of (U.V). (b) Find the marginal density of U. (c) Find...
1. Consider the joint probability density function 0<x<y, 0<y<1, fx.x(x, y) = 0, otherwise. (a) Find the marginal probability density function of Y and identify its distribution. (5 marks (b) Find the conditional probability density function of X given Y=y and hence find the mean and variance of X conditional on Y=y. [7 marks] (c) Use iterated expectation to find the expected value of X [5 marks (d) Use E(XY) and var(XY) from (b) above to find the variance of...
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)?
(3x, The joint density function of X and Y is given by 0 Sy sxs1 f(x, y) = 0, otherwise. a) Use the distribution function technique to find the distribution function of W = X-Y. For 50% of the points, you may use the transformation technique, which is longer. >) Find the probability density function of W. Find the expected value E(W). )