8. A factory is supplied with grain at the beginning of each week. The weekly demand X, thousanfd tonnes for grain from this factory is a continuous random varibale having the probability density function given by. Find the mean value. Express your answer in 3 decimal place value f(x) = 0 2(1-x) for 0≤x≤1 otherwise

8. A factory is supplied with grain at the beginning of each week. The weekly demand X, thousanfd tonnes for grain from this factory is a continuous random varibale having the probability density function given by. Find the mean value. Express your answer in 3 decimal place value f(x) = 0 2(1-x) for 0≤x≤1 otherwise

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.2: Probability

Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...

See similar textbooks

Similar questions

The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the conditional probability of the event E, getting a six, given that the event F, getting an even number, has occurred is P(EF)=___________.
Suppose an electric-vehicle manufacturing company estimates that a driver who commutes 50 miles per day in a particular vehicle will require a nightly charge time of around 1 hour and 30 minutes (90 minutes) to recharge the vehicle's battery. Assume that the actual recharging time required is uniformly distributed between 70 and 110 minutes. (a) Give a mathematical expression for the probability density function of battery recharging time for this scenario. f(x) = , 70 ≤ x ≤ 110 , elsewhere
Suppose an electric-vehicle manufacturing company estimates that a driver who commutes 50 miles per day in a particular vehicle will require a nightly charge time of around 1 hour and 40 minutes (100 minutes) to recharge the vehicle's battery. Assume that the actual recharging time required is uniformly distributed between 80 and 120 minutes. (a) Give a mathematical expression for the probability density function of battery recharging time for this scenario. f(x) = , 80 ≤ x ≤ 120 , elsewhere (b) What is the probability that the recharge time will be less than 109 minutes? (c) What is the probability that the recharge time required is at least 91 minutes? (Round your answer to four decimal places.) (d) What is the probability that the recharge time required is between 90 and 100 minutes?
Suppose that X is a continuous random variable with a probability density function is given by f(x)= 25 when x is between -2 and 2, and f(x)=0 otherwise. a.)Find E(X2), where X is raised to the power 2 b.) Find Var(2X+2)
Suppose that ƒ is a uniform joint probability density function on0 ≤ x 6 2, 0 ≤ y < 3. What is the formula for ƒ? What is theprobability that X < Y?
Suppose that the continuous random variable X has cumulative distribution function given by F(x)= 0, if x < sqrt(2); x2-2, if sqrt(2) <= x <= sqrt(3); 1, if sqrt(3) <= x Find the probability density function of X.
If the random variable T is the time to failure of a commercial product and the values of its probability den-sity and distribution function at time t are f(t) and F(t), then its failure rate at time t is given by f(t)1 − F(t). Thus, thefailure rate at time t is the probability density of failure attime t given that failure does not occur prior to time t.(a) Show that if T has an exponential distribution, thefailure rate is constant. (b) Show that if T has a Weibull distribution (see Exer-cise 23), the failure rate is given by αβt β−1.
Suppose that the joint density function of the random variables X and Y is f(x,y)=k(1+2y), if 7<x<13 and 0<y<1, and f(x,y)=0, otherwise. Show that the marginal distribution of X is g(x)=c, if 7<x<13, and g(x)=0 otherwise. Enter the value of c. Hint: Of course, first, you need to find the value of k. Round your answer to a number with two decimal digits after the decimal point. For example if your answer is 1/40, which is equal to 0.025, then you should enter 0.03. (Do NOT use decimal comma; 0,03 would be wrong.)
Alex decides to sell his old guitar, and sequentially receives bids from potential buyers. The minimum price that he will accept to sell his guitar for is £500. Let {Xn, n ≥ 0} denote the sequence of independent and identically distributed bids that Alex receives, and assume that each Xn has the following probability density functionfX(x) = (1/400)e-x/400 for x ≥ 0. Let N denote the number of bids that Alex obtains before selling his guitar i.e., Alex sells his laptop to the Nth bid. Showing your full working, (a) find E[N]. (b) find E[XN].
Let X be a random variable with probability density function f(x) = c(8x-x^2) if 0<x<8 otherwise f(x) = 0 What's c? Also, what's the cumulative distribution function of X on 0<x<8?
Suppose that a study of a certain computer system reveals that the response time, in seconds, has an exponential distribution with density curve f(x) = (1/3)e(-x/3) for x > 0 and f(x) = 0 otherwise. What is the probability that response time exceeds 5 seconds? What is the probability that response time exceeds 10 seconds?
let x denotes the percentage of time out of 40 hour workweek that a call center agent is serving a client by answering phone calls, suppose that x has probability density function defin by f(x)=3x^2 for 0< x < 1. find the mean and variance of x