Waiting Time At a certain supermarket, the amount of wait time at the express lane is a random variable with density function f(x) = 11/[10(x + 1)*], 0 < x s 10. (See Fig. 8.) Find the probability of having to wait less than 4 minutes at the express lane. 1.1 11 S(x) 10(x + 1)? 10 Figure 8 A density function.
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- A Troublesome Snowball One winter afternoon, unbeknownst to his mom, a child bring a snowball into the house, lays it on the floor, and then goes to watch T.V. Let W=W(t) be the volume of dirty water that has soaked into the carpet t minutes after the snowball was deposited on the floor. Explain in practical terms what the limiting value of W represents, and tell what has happened physically when this limiting value is reached.Q1)Losses in 1993 follow the density function fX(x) = 3x−4,x > 1 where x is the loss in millions of dollars. Inflation of 10% impacts all claims uniformly from 1993 to 1994. Determine the cdf of losses for 1994 and use it to determine the probability that a 1994 loss exceeds 2,200,000.A random variable X has the probability density function defined by f(x) = kx, 0 ≤ x ≤ 2. a. Find P(X>1). b. What is the probability density function of Y = 8X2? c. What is the expected value of Y?
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- A random variable Y has a probability density function f(y) = A(y − 1.5) over the state space−2 ≤ y ≤ 3, where A is a constant. Calculate the median of the random variable Y.Do you dislike waiting in line? A supermarket chain has used computer simulation and information technology to reduce the average waiting time for customers at 2,300 stores. Using a new system, which allows the supermarket to better predict when shoppers will be checking out, the company was able to decrease average customer waiting time to just 28 seconds. (a)Assume that supermarket waiting times are exponentially distributed. Show the probability density function of waiting time at the supermarket. f(x) = x ≥ 0 elsewhere (b) What is the probability that a customer will have to wait between 30 and 45 seconds? (Round your answer to four decimal places.) (c) What is the probability that a customer will have to wait more than 2 minutes? (Round your answer to four decimal places.)Martian potatoes begin to sprout very quickly after planting. Suppose X is the number of days after planting until a Martian potato sprouts. Then X has the following probability density function: f(x)= 2/7e−x + 3/14e−x/2 + 1/14e−x/4 for 0 ≤ x ≤ ∞ and 0 otherwise. h) What is the probability that X is more than 2 standard deviations above its expected value? j) What is the probability that X is within 1 standard deviation of its expected value? k) What is the probability that X = .6?