A pumping station operator observes the demand for water at 4 pm each day can be

Question

A pumping station operator observes the demand for water at 4 pm each day can be modeled as an exponential random variable with a mean of 250 cubic feet per second (efs). (a) If X is the demand at 4 pm on a randomly selected day, then find P(x > 300 efs). (b) What is the likelihood that the demand will exceed 300 efs 2 days in a row? (Assume that the days are independent) (c) what is the water-producing capacity that the station should keep on line for 4 pm so that the demand will exceed this capacity only 1 percent of the time ? In a town voters were surveyed and classified according to their level of education, X which takes on values 0 or 1 or 2, and their voting preference Y which also takes on values 0, 1 or 2. The joint probability function p(x, y) = p (X=x, Y=y) is given as follows. a. Find the marginal probability function for X and Y b. Find E[X/y = 2] c. Let X_1 and X_2 denote the proportion of time that employee I and II, respectively spend doing their job. The joint frequency for X_1 and X_2 is modeled with d. Find p(x_1 25) e. Calculate E(X_1|X_2) and write out the integrals (without computing) needed to find the covariance cov(x_1, x_2)

Explanation / Answer

a)

P(y=0)=(16+10+19)/103

p(y=1)=(8+17+15)/103

P(y=2)=(3+6+9)/103

P(X=0)=(16+8+3)/103

p(X=1)=(10+17+6)/103

P(X=2)=(19+15+9)/103


b) 0*(3/103)+1*(6/103)+2*(9/103)

c)Basically, two random variables are jointly continuous if they have a joint probability density function.

d) the probabilty is 0


Only 1st four parts.

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