Let the probability density of X be given by f (x) otherwise a) the cdf (Note:...
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)...
7. Let X a be random variable with probability density function given by -1 < x < 1 fx(x) otherwise (a) Find the mean u and variance o2 of X (b) Derive the moment generating function of X and state the values for which it is defined (c) For the value(s) at which the moment generating function found in part (b) is (are) not defined, what should the moment generating function be defined as? Justify your answer (d) Let X1,...
Distributions Consider the function f(x)3+1-2-4 0334 (a) Can this function be used as a probability density function? If not, normalize it such that it can, and let that be p(x) (b) Create a CDF of your probability density function, p(x) (c) Compute the expected value and variance of p(z) (d) What is the 90th percentile value of p() Distributions Consider the function f(x)3+1-2-4 0334 (a) Can this function be used as a probability density function? If not, normalize it such...
Find mean and variance of a random variable whose probability density function is given by f(x) = C(x + 1) when -1<= x <=1 otherwise f(x) = 0 Find C values also.
5. Let the joint probability density function of X and Y be given by, f(x,y) = 0 otherwise (a) Find the value of A that makes f (x, y) a proper probability density function (b) Calculate the correlation coefficient of X and Y. (c) Are X and Y independent? Why or why not?
Let X be a random variable with the following probability density function: 0 otherwise. Using following relationship ueudu a. Show that fy (y) is a valid probability density function b. Show that the moment generating function My (t) =-for t 2 (2-t) c. Obtain the first and second raw moments. d. Using these raw moments determine the mean and variance Let X be a random variable with the following probability density function: 0 otherwise. Using following relationship ueudu a. Show...
Let X be a r.v. with probability density function f(x)-e(4-x2), -2 < otherwise (a) What is the value of c? (b) What is the cumulative distribution function of X? (c) What is EX) and VarX
2. Let X and Y be continuous random variables with joint probability density function fx,y(x,y) 0, otherwise (a) Compute the value of k that will make f(x, y) a legitimate joint probability density function. Use f(x.y) with that value of k as the joint probability density function of X, Y in parts (b),(c).(d),(e (b) Find the probability density functions of X and Y. (c) Find the expected values of X, Y and XY (d) Compute the covariance Cov(X,Y) of X...
2. The random variable X has probability density function f given by f(x) 0 otherwise. (a) Is X continuous or discrete? Explain. (b) Calculate E(X). (c) Calculate Var(2X 9).
1. (10 points) Let X be a continuous random variable with the probability density function given by f(x)-4z if 0SaS1 and O otherwise (a) Find P(X sjIx> j) (b) Find the expectation and variance of X