The lifetime, X, of a CPU in the Edsel computer, measured in months, has the following probability density function: f(x)= 338 x3 for x ≥ 13 and 0 otherwise. g) What is the expected value of 1/X? h) What is the probability that X is less than its expected value? i) What is the expected value of the square root of X?

A scout on a camping trip is requested to find some dry sticks of length at most one metre to use as firewood. A model for the distribution of the lengths, X, in metres, of sticks that she brings back to the camp has probability density function f(x) = VT, 0< x < 1. 0 < x < 1. According to the model, what is the mean length of the sticks that the scout brings back?

A random variable X has the probability density function of the attached graph (see attached photo): a) What is the expected value of X? b) Compute P(-500 < X < -250).

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. 1 f(x) = x, [5,9] 28 a) Find the mean. %3D (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 variable x is within one standard deviation of the mean. The probability is. (Round to three decimal places as needed.)

The density function of the continuous random variable X is shown below. When c≈ 0.163, Find: (1) the mode, (2) the median, and (3) the mean. Jcsin (2 -0.2x) for 1≤ x ≤ 10 f(x) = {0 elsewhere mahamdy@uoanbar.edu.iq

Show that the expectation of the exponential distribution with param- eter A is 1/A.