The solution to this problem is given below
For the probability density function f defined on the random variable x, find (a) the mean...
3 The probability density function of a random variable on the interval [9, 16] is f(x) = x. Find the following values. a. Find the expected value The expected value is (Round to two decimal places as needed.) b. Find the variance. The variance is (Round to two decimal places as needed.) c. Find the standard deviation The standard deviation is (Round to two decimal places as needed.) d. Find the probability that the random variable has a value greater...
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
x A probability density function of a random variable is given by f(x) = @ ż on the interval [4, 8]. Find the expected value, the variance, and the standard deviation. The expected value is u (Round to two decimal places as needed.) The variance is Var(x)=0 (Round the final answer to two decimal places as needed. Use the expected value rounded to two decimal places. Do not round any other intermediate values.) The standard deviation is o (Round the...
X 1 A probability density function of a random variable is given by f(x) = 10 - a on the interval [2, 8]. Find the expected value, the variance, and the standard deviation. The expected value is u ~ (Round to two decimal places as needed.) The variance is Var(X) ~ (Round the final answer to two decimal places as needed. Use the expected value rounded to two decimal places. Do not round any other intermediate values.) The standard deviation...
х 1 A probability density function of a random variable is given by f(x) = standard deviation. wi- on the interval (1, 3). Find the expected value, the variance, and the 2 The expected value is u (Round to two decimal places as needed.) The variance is Var(x). (Round the final answer to two decimal places as needed. Use the expected value rounded to two decimal places. Do not round any other intermediate values.) The standard deviation is on (Round...
1 The life (in years) of a certain machine is a random variable with probability density function defined by f(x) = 5 + 2 vx for x in (1, 25). 136 A. Find the mean life of this machine. The mean life is approximately years. (Round to two decimal places as needed.) B. Find the standard deviation of the distribution. The standard deviation is approximately years. (Round the final answer to two decimal places as needed. Use the expected value...
Find the mean and variance of the random variable X with probability function or density f(x). 3. Uniform distribution on[0,2pi]. 4. Y= square root 3(X-u) /pi with X as in problem 3.
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.
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