Assume the life of an electronic component in hours is a random variable with the following density function: 9. f(x)-(01 ge-./soo, elsewhere. Find the following: (a) The mean life of the electronic...
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
3. If a dealers profit, in units of $5000, on a new automobile can be looked upon as a random variable X having the density function f(x) = 2(1 - ), o if 0<x<1, elsewhere. (a) Find the average profit per automobile. (b) Find the standard deviation ox. (c) Find the variance of the dealers profit. (d) Demonstrate that Chebyshevs theorem holds for k = 2 with the density function above (e) What is the probability that the profit exceeds...
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...
Assume the length X in minutes of a particular type of telephone conversation is a random variable with probability density function f(x) = {1/5 e^x/5, x > 0 0, elsewhere (a) Determine the mean length E (X) of this type of telephone conversation. (b) Find the variance and standard deviation of X. (c) Find E [(X + 5)^2].
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
Problem 3. The random variable X has density function f given by 0, elsewhere (a) Assuming that 6 0.8, determine K (b) Find Fx(t), the c.d.f. of X (c) Calculate P(0.4 <X < 0.8)
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.
Problem 3. The random variable X has density function f given by 0,elsewhere (a) Assuming that θ-0.8, determine K (b) Find Fx(t), the c.d.f. of X (c) Calculate P(0.4sX s 0.8)
3. (25 pts) The life X, in hours, of a certain kind of electronic part has a probability density function given by fory 2100 f,(y) o, fory <100 (A) What is the probability that a part will survive 250 hours of operation? (B) Find the expected value of the random variable (C) Find the variance of the random variable if the probability density function is given by y 2100 0, y<100.