x/3 The life (in months) of a certain electronic computer part has a probability density function defined by f(x) = for x in [0, o). Find the probability that a randomly selected component will last the following lengths of time. A. At most 12 months. The probability that the component will last at most 12 months is (Round to four decimal places as needed.)

Assume that the coin is weighted so that Pr[H]=5/9, and that the coin is flipped until a head appears, or 3 consecutive tails appear. The random variable XX is defined to be the total number of flips of the coin.   Part 2 Fill in the table below to complete the probability density function. Be certain to list the values of XX in ascending order

let X denotes the percentage of time out of a 40-hour workweek that a call center agent is directly serving a client by answering phone calls. Suppose that X has a probability density function defined by f(x) =3x² for 0 ≤ x ≤ 1. Find the mean and variance of X. Interpret the results.

Let y be the random variable with the time to hear an owl from your room's open window (in hours). Assume that the probability that you still need to wait to hear the owl after y hours is one of the following: the probability is given by 0. 47e-4y + 0. 52e-5y Find the probability that you need to wait between 2 and 4 hours to hear the owl, compute and display the probability density function graph as well as a histogram by the minute. Compute and display in the graphics the mean, variance, and quartiles of the waiting times. Please pay attention to the various units of time!

1. or a cumulative distribution function (edf). Decide if the function graphed below is a probability density function (pdf) 2c 4 8.

This is Involving drawing markers from a box of markers with ink and markers without ink. Assume that the box contains 17 markers: 14 that contain ink and 3 that do not contain ink. A sample of 4 markers is selected and a random variable Y is defined as the number of markers selected which do not have ink. Fill in the table below to complete the probability density function. Be certain to list the values of Y in ascending order.

The random variables X and Y have a joint probability density function given by f(x, y) = way, 0 < x < 3 and 1 < y < x, and 0 otherwise.

Suppose our population is made up of the 12 individuals whose monthly INCOME: 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51. 1. Find the ff. probabilities: P (X-bar < 46) P (44 < X-bar < 47) P (48 < X-bar < 50)2. Derive a graph of the probability density function.