Select a stock such as Apple, Dell, or Microsoft and use the Jarque-Bera test to determine if the annual daily rates of return for a particular year follow a normal distribution.

A random sample of 50 students was asked to estimate how much money they spent on textbooks in a year. The sample skewness of these amounts was found to be 0.83 and the sample kurtosis was 3.98. Test at the 10% level the null hypothesis that the population distribution of amounts spent is normal.

A 6-cm-diameter shaft rotates at 3000 rpm in a 20-cm- long bearing with a uniform clearance of 0.2 mm. At steady operating conditions, both the bearing and the shaft in the vicinity of the oil gap are at $50^\circ C,$ and the viscosity and thermal conductivity of lubricating oil are $0.05 \mathrm{N} \cdot \mathrm{s} / \mathrm{m}^{2} \text { and } 0.17 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}$ By simplifying and solving the continuity, momentum, and energy equations, determine (a) the maximum temperature of oil, (b) the rates of heat transfer to the bearing and the shaft, and (c)the mechanical power wasted by the viscous dissipation in the oil.

In a period of 100 minutes there were a total of 190 arrivals at a highway toll booth. The accompanying table shows the frequency of arrivals per minute over this period. Test the null hypothesis that the population distribution is Poisson.

$$\begin{array}{lccccc} \hline \text { Number of arrivals } & & & & & \\ \text { in minutes } & 0 & 1 & 2 & 3 & 4 \text { or more } \\ \hline \text { Observed frequency } & 10 & 26 & 35 & 24 & 5 \\ \hline \end{array}$$

Hot water at $90^\circ C$ enters a 15-m section of a cast iron pipe $(k= 52W/m \cdot K)$ whose inner and outer diameters are 4 and 4.6cm, respectively, at an average velocity of 1.2 m/s. The outer surface of the pipe, whose emissivity is 0.7, is exposed to the cold air at $10^\circ C$ in a basement, with a convection heat transfer coefficient of $12 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}.$ Taking the walls of the basement to beat $10^\circ C$ also, determine (a) the rate of heat loss from the water and (b) the temperature at which the water leaves the basement.

Saturated water vapor at $100^{\circ} \mathrm{C}$ condenses in the shell side of a one-shell and two-tube heat exchanger with a surface area of $0.5 \mathrm{m}^{2}$ and an overall heat transfer coefficient of $2000 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}.$ Cold water $\left(c_{p c}=4179 \mathrm{J} / \mathrm{kg} \cdot \mathrm{K}\right)$ flowing at 0.5 kg/s enters the tube side at $15^{\circ} \mathrm{C},$ determine the outlet temperature of the cold water and the heat transfer rate for the heat exchanger.

A user can directly connect to a server through either long-range wireless or a twisted-pair cable for transmitting a 1500-bytes file. The transmission rates of the wireless and wired media are 2 and 100 Mbps, respectively. Assume that the propagation speed in air is $3\times 10^8$ m/s while the speed in the twisted pair is $2\times 10^8$ m/s If the user is located 1 km away from the server, what is the nodal delay when using each of the two technologies?

The number of times a machine broke down each week was observed over a period of 100 weeks and recorded in the accompanying table. It was found that the average number of breakdowns per week over this period was 2.1. Test the null hypothesis that the population distribution of breakdown is Poisson.

$$\begin{array}{lcccccc} \hline \text { Number of breakdowns } & 0 & 1 & 2 & 3 & 4 & 5 \text { or more } \\ \hline \text { Number of weeks } & 10 & 24 & 32 & 23 & 6 & 5 \\ \hline \end{array}$$

The upper surface of a metal plate is being cooled with parallel air flow while its lower surface is subjected to a uniform heat flux of $810 \mathrm{W} / \mathrm{m}^{2}.$ The air has a free stream velocity and temperature of 2.5 m/s and $15^{\circ} \mathrm{C},$ respectively. Determine the surface temperature of the plate at x = 1.5 m from the leading edge.

The upper surface of a metal plate is being cooled with parallel air flow while its lower surface is subjected to a uniform heat flux of $810 W/m^2.$ The air has a free stream velocity and temperature of 2.5 m/s and $15^\circ C,$ respectively. Determine the surface temperature of the plate at x = 1.5 m from the leading edge.

A random sample of statistics professors was asked to complete a survey including questions on curriculum content, computer integration, and software preferences. Of the 250 responses, 100 professors indicated that they preferred software package M and 80 preferred software package E, whereas the remainder were evenly split between preference for software package S and software package P. Do the data indicate that professors have a preference for any of these software packages?

Consider a packet of length L which begins at end system A and travels over three links to a destination end system. These three links are connected by two packet switches. Let $d_i, s_i$ and $R_i$ denote the length, propagation speed, and the transmission rate of link $i$, for $i=1,2,3$. The packet switch delays each packet by $d_{p r o c}$. Assuming no queuing delays, in terms of $d_i, s_i, R_i$, ( $i=1,2,3)$, and $L$, what is the total end-to-end delay for the packet? Suppose now the packet is 1,500 bytes, the propagation speed on all three links is $2.5$. $10^8 \mathrm{~m} / \mathrm{s}$, the transmission rates of all three links are $2 \mathrm{Mbps}$, the packet switch processing delay is $3 \mathrm{msec}$, the length of the first link is $5,000 \mathrm{~km}$, the length of the second link is $4,000 \mathrm{~km}$, and the length of the last link is $1,000 \mathrm{~km}$. For these values, what is the end-to-end delay?

Consider the throughput example corresponding to earlier Figure. Now suppose that there are M client-server pairs rather than 10. Denote Rs, Rc, and R for the rates of the server links, client links, and network link. Assume all other links have abundant capacity and that there is no other traffic in the network besides the traffic generated by the M client-server pairs. Derive a general expression for throughput in terms of Rs, Rc, R, and M.

Suppose users share a 3 Mbps link. Also suppose each user requires 150 kbps when transmitting, but each user transmits only 10 percent of the time.

a. When circuit switching is used, how many users can be supported?

b. For the remainder of this problem, suppose packet switching is used. Find the probability that a given user is transmitting.