Given the accompanying information for a fanciful hero universe:

Flying Telepathy Super Strength

Female 97 92 77

Male 24 64 3

Dissemination of Super Power by Gender

What is the observational likelihood that a haphazardly chosen hero will have clairvoyance?

Answer in decimal structure. Round to 3 decimal places on a case by case basis

An overview asked 816 school green beans whether they had been to a film or eaten in a caf during the previous week. The accompanying data was acquired: 391 green beans had been to neither a film nor an eatery, and 266 had been to a film. In the event that 92 of the individuals who had been to a film had not been to a caf, what number of the reviewed green beans had been to the accompanying?

(a) both a film and a caf

(b) a film or a caf

(c) a caf

(d) a caf however not a film

A rescue vehicle goes to and fro, at a steady explicit speed v, along a street of length L. We may show the area of the emergency vehicle at any second on schedule to be consistently circulated over the span (0, L). Additionally at any second on schedule, a mishap (not including the emergency vehicle itself) happens at a point consistently disseminated out and about; that is, the mishaps distance from one of the fixed stopping points is likewise consistently conveyed over the stretch (0, L). Expect the area of the mishap and the area of the rescue vehicle are free.

Assuming the emergency vehicle is fit for guaranteed U-turns, register the CDF and PDF of the ambulances head out time T to the area of the mishap.

Alex Mason has a wide-bending, uphill carport prompting

~28~

his carport. When there is a weighty snow, Alex enlists a nearby

woodworker, who digging tools snow as an afterthought in the colder time of year, to

scoop his carport. The snow shoveler charges $30 to

scoop the carport. Following is a likelihood conveyance

of the quantity of hefty snows each winter.Alex is thinking about the acquisition of another self-pushed

snowblower for $575 that would permit him, his better half, or his

kids to clear the carport after a snow. Talk about what

you believe Alex's choice ought to be and why.

Weighty Snows Probability

1 1.12

2 0.19

3 0.24

4 0.22

5 0.13

6 0.08

7 0.02

1) Chemical Equilibrium of a Diatomic Dissociation Reaction. In class we calculated the equilibrium constant for the gas phase dissociation reaction: Na, (g) - 2Na(g) using statistical mechanics. We found the "activity" coefficient equilibrium constant K [such that K = (pxa/p") /(pxa /p")] at 1000K, namely, K =2.4. Repeat this calculation at the two temperatures 7=800, 1200K. [Molecular constants relevant to the problem are provided in the class notes.[2] The joint probability density function of random variables X and Y is fxy (x, y) = 10. [cx, y's x s 4, ly) $2 otherwise Find the (a) [10 pts] value of c (b) [15 pts] mean of X when Y=1. [3] (parts (a) and (b) are separate questions) (Part (a)) [13 pts] The joint probability density function of random variables X and Y is fry(x, y) = 8' O S y S x S 5,0 Sys2 O otherwise Find the probability density function of W-Max(X,Y). (Part (b)) [12 pts] X and Y are jointly Gaussian random variables. It is known that: the mean of X is 2 . the variance of X is 9 the correlation coefficient of X and Y is 0.25 . the linear regression of the value of X when Y=y (i.e. &, (y)) is given by &L(y) = 0.75y + 6 Find the probability that X>4 when Y=7.2.22 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-Question 4 E = EEbond + EEang + Etors + [ Eww + _ Eelectrostatic bonds angles forsions ann pairs aim pairs A general equation for a molecular mechanics force field is shown above: a) Explain why molecular mechanics force fields are described as being 'empirical". b) Explain how Ebond is calculated c) Explain how Eelectrostatic is calculated. d) Explain how Ever is calculated. e) The calculation Execrostatic is the most time consuming part of molecular mechanics calculations. Explain why this is so. Explain how the amount of computation necessary to calculate Eelectrostatic can be reduced. What problems can these approximations cause? Describe two approximations that are made to speed up molecular mechanics calculations