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
Show that the function f(x)=1/(x^2+π^2 ) can be taken as a probability density (distibution) function of...
Q1) (20 Mark) The probability density function of a random variable X is given by: f(x) Cx-2 x21 1) Find the value of C 2) Find the distribution function F(X) 3) Find P(X > 3) 4) Find the mean and the standard deviation of the distribution
Q1) (20 Mark) The probability density function of a random variable X is given by: f(x) Cx-2 x21 1) Find the value of C 2) Find the distribution function F(X) 3) Find P(X > 3) 4) Find the mean and the standard deviation of the distribution
X is a continuous random variable, f(x) is the probability density function (pdf) of X, and F(x) is the cumulative distribution function of X. Then for any two numbers a and b with a < b, which of the following are true? Circle all correct answers. A. B. C. D. 5. If X is a normally distributed random variable with a mean of 36 and a standard deviation of 12, then the probability that X exceeds 36 is: A. .5000...
Homework help with 7.63 please 7.63 Let the random variable X have probability density function f(x)= -π/2 < x <π/2. Find the probability density function of Y sin X by the (a) cumulative distribution function technique, (b) transformation technique. dx1 Hint: The derivative oh-arcsiny is
The random variable X has probability density function k(x25x-4) 1<x<4 otherwise -{ f(x) 1. Show thatk. (5pts) Find 2. Е (X), (5pts) 3. the mode of X, (5pts) 4. the cumulative distribution function F(X) for all x. (5pts) 5. Evaluate P(X < 2.5). (5pts) 6. Deduce the value of the median and comment on the shape of the distribution (10pts)
For the probability density function f defined on the random variable x, find (a) the mean of x, (b) the standard deviation of x, and (c) the probability that the random variable x is within one standard deviation of the mean. f(x) = 1 30 x, [2,8] a) Find the mean. u = (Round to three decimal places as needed.) b) Find the standard deviation. = (Round to three decimal places as needed.) c) Find the probability that the random...
The random variable X has probability density function f (x) = k(−x²+5x−4) 1 ≤ x ≤ 4 or =0 1 Show that k = 2/9 Find 2 E(X), 3 the mode of X, 4 the cumulative distribution function F(X) for all x. 5 Evaluate P(X ≤ 2.5). 6 Deduce the value of the median and comment on the shape of the distribution.
2x 0<x<1 Let X be a continuous random variable with probability density function f(x)= To else The cumulative distribution function is F(x). Find EX.
22. Given a continuous random variable X with probability density function f(x) = {2x, if :05451 otherwise a. Find P(0.3< X< 0.6) b. Find the mean of X C. Find the standard deviation of X.
Let X be a random variable with probability density function a) Find the mean of X b) Find the standard deviation of X round to four decimal places. c) Let G = X2 Find the probability density function fG of G Show work for each part plz f(x) = { 1 x (3-X) it osx=2 Co otherwise