9. A factory is supplied with grain at the beginning of each week. The weekly demand X, thousanfd tonnes for grainfrom this factory is a continuous random varibale having the probability density function given by. Compute thevariance.express your answer in 4 decimal place value2(1-x) for 0≤x≤ 1f(x) = Lootherwise

Given function is f(x)={2(1-x) for 0≤x≤10 otherwise

Answered: A factory is supplied with grain at the…

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...

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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 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 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
A harried passenger will be several minutes late for a scheduled 10 A.M. flight to NYC. Nevertheless, he might still make the flight, since boarding is always allowed until 10:10 A.M., and boarding is sometimes permitted up to 10:30 AM. Assuming the end time of the boarding interval is uniformly distributed over the above limits, find the probability that the passenger will make his flight, assuming he arrives at the boarding gate at 10:25.
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].
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.
Carl decides to sell his old laptop on eBay, and sequentially receives bids from potential buyers. The minimum price that he will accept to sell his laptop for is $600. Let {Xn, n ≥ 0} denote the sequence of independent and identically distributed bids that Carl receives, and assume that each Xn has the following probability density function fX (x) = (1/400)e −x/400 for x ≥ 0. Let N denote the number of bids that Carl obtains before selling his laptop i.e., Carl sellshis laptop to the Nth bid. (a) Find E[N]. (b)Find E[XN ].
If X is a continuous variable in the range 3 > X > 0 and its distribution function is as follows: F ( x ) = k : ( x3 + x2) find the probability density function?
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 P, the price of a certain commodity (in dollars), and S, its total sales (in 10,000 units), are ran-dom variables whose joint probability distribution can be approximated closely with the joint probability density f(p,s) = 5pe−ps for 0.20 < p < 0.40,s > 00 elsewhereFind the probabilities that(a) the price will be less than 30 cents and sales willexceed 20,000 units;(b) the price will be between 25 cents and 30 cents andsales will be less than 10,000 units.
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.)
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?

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