2. (25 points) For the probability density function (pdn) sGr) rx) =10.08 x (0 5) x...
The distance X between trees in a given forest has a probability density function given f (x) cex/10, x >0, and zero otherwise with measurement in feet i) Find the value of c that makes this function a valid probability density function. [4 marks] ii) Find the cumulative distribution function (CDF) of X. 5 marks What is the probability that the distance from a randomly selected tree to its nearest neighbour is at least 15 feet. iii) 4 marks) iv)...
Show that the function f(x)=1/(x^2+π^2 ) can be taken as a probability density (distibution) function of a random variable X. Find p(X>π). Find also the cumulative distribution function F(x) of the random variable X. Find, finally, mean and standard deviation of the random variable X 1 Show that the function f(x) = can be taken as a probability density (distibution) x²+x² function of a random variable X. Find p(x > 1). Find also the cumulative distribution function F(x) of the...
1. (25 points) Consider the following probability density function and the random vector W. fxy(x,y)= 1/16 0 |x|52, lyls2 elsewhere X W=(x,y)" Li a) (5 points) Find and plot the conditional joint probability density function f wilx<0,y>o)(W|x<0, y>0) b) (5 points) Find and plot the conditional joint cumulative distribution function Fw1(x<0,y>0)(W|x<0, y>0) c) (5 points) Find E(W). d) (10 points) Find E(W x<0, y>0).
Q1: Suppose the probability density function of the magnitude X of a bridge (in newtons) is given by fx)-[e(1+3) sxs2 otherwise (a) Find the value of c. (b) Find the mean and variance (c) Find P(1 <x<2.25) (d) Find the cumulative distribution function.
1. 20 points Let X be a random variable with the following probability density function: f(x)--e+1" with ? > 0, ? > 0, constants x > ?, (a) 5 points Find the value of constant c that makes f(x) a valid probability mass function. (b) 5 points Find the cumulative distribution function (CDF) of X.
2. Let X have probability density function JX2) = 1/2 0<x< 1 3 < x < 4 otherwise Find the cumulative distribution function of X.
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...
Suppose that the probability density function of X is f(x) {cx3 0 1< x < 5 otherwise where c is a constant. Find P(X < 2).
Suppose that the probability density function of X is f(x) {cx3 0 1< x < 5 otherwise where c is a constant. Find P(X < 2).
Find the mean and variance of the random variable X with probability function or density f(x) f(x) = k(1 – x2) if –1 3x = 1 and 0 otherwise