Use the following information for all steps in this problem. Input all answers to three decimals places and do not input your answers as a percentage.

Alec is taking both a Statistics course and a Geography course this semester. The probability that he passes his Statistics course is 0.65. The probability that he passes his Geography course is 0.92. These two events (passing Statistics and passing Geography) are independent.

1. What is the probability he passes both classes?

2. What is the probability he passes one, but fails the other?

3. What is the probability he passes at least one

4. What is the probability he passes neither class?

5. What is the probability he passes Statistics and fails Geography?

6. What is the probability he passes Geography and fails Statistics?

Diane Bruns is the chairman of an enormous city. Recently, she has gotten worried about the likelihood that huge quantities of individuals who are drawing joblessness checks are furtively utilized. Her aides gauge that 40% of joblessness recipients fall into this class, yet Ms. Bruns isn't persuaded. She requests one from her helpers to lead a peaceful examination of 10 arbitrarily chose joblessness recipients. On the off chance that the city hall leader's aides are right, what is the likelihood that one or three of the researched people have occupations?

bank is keen on examining the quantity of individuals who utilize the ATM situated outside

its office late around evening time. By and large, 1.9 clients approach the ATM during any 10-minutes

span among 9pm and 12 PM. Distinguish the irregular variable in the above explanation and

recommend the suitable conveyance to investigate the idea of the irregular variable. Utilizing the

proposed answer, process the likelihood of precisely 4 clients utilizing ATM administrations in any

10 minutes span between 9 pm and 12 PM.

Likewise, process the likelihood of under 4 individuals utilizing the ATM during any 10 minutes

stretch between 9 pm and 12 PM.

A school teacher never completes his talk the hour's end and consistently completes his talks inside 2 min after the hour. Let X = the time that slips by between the hour's end and the finish of the talk and assume the pdf of X is as per the following:

f(x) = kx^2 if 0

(a) What is the likelihood that the talk proceeds past the hour for somewhere in the range of 30 and 90 sec? (Round your response to four decimal spots.)

~25~

(b) What is the likelihood that the talk proceeds for at any rate 105 sec past the hour's end? (Round your response to four decimal spots.)

Allow X to signify the measure of time a book on two-hour hold is really looked at, and assume the cdf is the accompanying. F(x) = 0 if x = 5. Utilize the cdf to get the accompanying. (On the off chance that important, round your response to four decimal spots.)

(d) What is the middle checkout span ? [solve 0.5 = F()]. (Answer isn't 3.536.)

(e) Obtain the thickness work f(x). (Answer is 2x/25.)

(f) Calculate E(X). (Answer isn't 3.333.)

1. (25 pts.) The class registrations of 50 mechanical engineering students are analyzed. It is found that: *5 students take all three subjects (Dynamics, Statistics, and Fluid Mechanics), Dynamics * 18 students take Dynamics and Statistics, * 9 students take Dynamics and Fluid Mechanics, *7 students take Statistics and Fluid Mechanics, * 29 students take Dynamics, * 15 students take Fluid Mechanics, * 1 student takes none of the three. Statistics Fluid (1) How many students take only Statistics? (2) What is the probability that a student selected at random takes all three, given she/he takes Statistics? (3) If one of the students who take at least two of the three courses is chosen at random, what is the probability that he or she takes all three courses? (4) n(Statistics ( Dynamics) = ? (5) n Statistics ~ Fluid Dynamics) = ?2.22 Let A = 6 9 4 4 (a) Find the spectral decomposition of A as in (2.109). (b) Find the spectral decomposition of A and show that the diagonal matrix of eigenvalues is equal to the square of the matrix D found in part (a), thus illustrating (2.115). (c) Find the spectral decomposition of A- and show that the diagonal matrix of eigenvalues is equal to the inverse of the matrix D found in part (a), thus illustrating (2.116). 2.23 Find the singular value decomposition of A as in (2.117), where A NAN 2.24 If j is a vector of I's, as defined in (2. 1 1), show that the following hold-Statistical mechanics provides equations that relate physical properties to the intermolecular forces or intermolecular potential energies. We wish to calculate the properties of an organic liquid using molecular simulation - molecular dynamics (MD) and/or Monte Carlo (MC) simulation, and have available an equation for the intermolecular potential energy for the liquid. The properties to be calculated are: internal energy (J), pressure (Pa), radial distribution function, g(r) , the self-diffusion coefficient (m /s) and the viscosity (kg/(m*s)) of the system. (a) Please briefly describe the principles of both MD and MC simulations. What are the main differences between MC and MD? (b) In using MD you must first decide on the magnitude of the time step. What are the considerations in determining a suitable time step? (c) Which of five properties of the system can be calculated only from MD simulation? Explain the reason. (d) Which of five properties of the system can be calculated from both MD and MC simulation?Thermodynamics 1. .08 Kg of air at 700 Kpa and 800 C is expanded adiabatically to 100Kpa in a closed system. Taking 8 1.4 calculate the following: a. the final temperature b. the work transfer c. the change in internal energy 2. 0.2 Kg of gas at 100 is expanded isothermally and reversible from 1 Mpa pressure to 100KPa. Take Cv= 718 J/Kg.K and R=2871/Kg.K. Calculate: a. the work transfer b. the change in internal energy c. the heat transfer