Kindly resolve. keyboard operator averages 2 errors per page of newsprint and if these errors follow a Poisson process, what is the probability that

a. exactly 4 errors will be found on a given page?

b. at least 2 errors will be found on a given page?

2. Crossville police records show that there has been an average of 4 accidents per week on

Crossville's new freeway. If these accidents follow a Poisson process, what's the probability that

a. the police must respond to exactly 6 accidents in a week?

b. that the police must respond to fewer than two accidents in a week?

3. Bigrig Trailer Corporation uses large panels of sheet metal in the manufacture of tandem trailers. If there is an average of 3 blemishes per panel and if the blemishes follow a Poisson process, what is the probability that

a. there will be no blemishes on a given panel?

b. there will be exactly 2 blemishes on a given panel?

4. The student health center at Oklahoma State University in Stillwater treats an average of 10 cases of severe alcohol poisoning a semester. Assuming a Poisson distribution, find the probability that

a. that the health center treats twelve cases of severe alcohol poisoning a semester.

b. the health center treats fewer than 5 cases of severe alcohol poisoning a semester.

c. the health center treats more than 15 cases of severe alcohol poisoning a semester.

Derive an expression for the vertical distribution of density in the troposphere, p(z), assuming hydrostatic conditions, and a linear distribution of tropospheric temperature, with a lapse rate I. Graph your results.Which of the following distributions of charge produces an electric field of magnitude independent of the distance from the charge distribution O Uniform surface distribution of charge on infinitely extended plane surface. Point charge O Two point charges of the same magnitude and opposite signs, separated by a distance d. O Uniform linear distribution of charge along an infinitely long straight wire9. Let X be a random variable denoting grade in a math course and Y be a random variable denoting grade in a statistics course with joint pdf of f(x, y) = [x + 2y x,ye (0,1) 0 otherwise What is the probability that a student received a grade of B or better (>80%) in the math course and statistics course?2. Loads X, and X2 are independent random variables applying on a cantilever beam as shown in Fig. P7.2. The probability density functions for these random variables are f, and fo, re- spectively, and described as: f ( x ) = C 70 OSX, $70 KN f (x ) = C 90 OSX, $90 kN in which q and c, are constants