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1. Data indicate that the number of traf?c accidents in Berkeley on a rainy day is a Poisson random variable with mean 9, whereas on a dry day it is a Poisson random variable with mean 3. Let X denote the number of traf?c accidents tomorrow. If it will rain tomorrow with probability 0.6, ?nd
(a) E[X];
(b) P{X = 0};
(c) Var(X).
2. The number of storms in the upcoming rainy season is Poisson distributed but with a parameter value that is uniformly distributed over (0, 5). That is, A is uniformly distributed over (0, 5), and given that A = λ, the number of storms is Poisson with mean λ. Find the probability there are at least three storms this season.
Let P be the transition matrix of an ergodic Markov chain and P∗ the reverse transition matrix. Show that they have the same fixed probability vector w.
Write an expression for the probability that during a given 1-min period, all of the operators receive exactly the same number of requests.
Ailín is the recently appointed purchasing manager of firm manufacturing folding bicycles.
An employee may retire at any age from 63 to 65, with a reduction in pension income of 5% per year. Find a formula for the actuarial present value of the pension benefits.
Independently of all the others. The system is operational if no two adjacent lamps fail. Obtain an expression for system reliability.
Modify the program ErgodicChain so that you can compute the basic quan- tities for the queueing example of Exercise 11.3.20. Interpret the mean recur- rence time for state 0.
Compute the coefficients of the regression line, interpret the coefficients - sample of 10 games and recorded the number of beers sold and the temperature in the middle of the game.
To test whether there is a significant mean difference among the three.
a poll was conducted that asked 1015 people how many books they had read in the past year. x13.3 books and s16.6 books
Calculate a 3-period moving average for period 7. Compute the MAD of the forecast.
Using the data below., develop a multiple regression model to predict score (rating) based on restaurant type (0 = Italian and 1 = Seafood/Steakhouse) and price of a meal in dollars
We suspect that the average fasting blood sugar level of Mexican Americans is 108. A random sample of 225 clinic patients (all Mexican American) yields a mean blood sugar level of 119 (S2 = 100). Test the hypothesis that µ. = 108. What is the ..
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