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Exercise 2. A service facility charges a $20 fixed fee plus $25 per hour of service up to 6 hours, and no additional fee is charged for service exceeding 6 hours. Suppose that the service time $\tau$ is equally likely to be any number of hours in {1,2,3,4,..., 10} hours (Assume that it takes some integer number of hours). Let X represent the cost of service in the facility. (a) Find and sketch the probability mass function for X. (b) Find and sketch the cumulative distribution function for X. (c) What is the probability that you end up paying less than or equal to $70 for service? Answer this part two different ways: • Using your answer to part (b). • Finding the time (call it $\tau_0$) at which the service would cost exactly $70 and then finding the probability that $\tau \le \tau_0$. (d) What is the expected value (or mean) of X? (e) The repair shop calls after 4.5 hours and tells you that your car is not ready yet; hence, this is going to cost you at least $145. Given this information, come up with a new probability mass function for how much it will cost. ```

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How to design a hydrogen cylinder tank that has diameter of 20cm, hold 20l of hydrogen, using the 7075 aluminium? I choosed the pressure inside the tank to be 500MPa. The yield strength and fracture toughness should be taken into account, and leak-before-break condition should be satisfied.

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Let $ X_{i} \sim \operatorname{Exp}(1), i=1,2, \ldots $, independently. Show that $ Y=X_{1}+X_{2} $ is not an exponential r.v. Hint: Recall from class when we solved \#8.2. Let $ f_{1}\left(x_{1}\right) $ and $ f_{2}\left(x_{2}\right) $ denote the exponential p.d.f. for $ X_{1} $ and $ X_{2} $, respectively. Which of the following statements is a valid argument? Mark the correct choice. (a) $ f_{1}\left(x_{1}\right)=e^{-x_{1}} $ and $ f_{2}\left(x_{2}\right)=e^{-x_{2}} \Longrightarrow f_{Y}(y)=e^{-x_{1}}+e^{-x_{2}} $ (b) $ f_{Y}(y)=e^{f_{1}\left(x_{1}\right)+f_{2}\left(x_{2}\right)}=e^{f_{1}\left(y-x_{2}\right)+f_{2}\left(y-x_{1}\right)} $ (c) $ f_{Y}(y)=\int_{0}^{y} e^{-\left(y-x_{1}\right)} e^{-x_{1}} d x_{1}=y e^{-y} $ (d) Use the change of variable formula, $ f_{Y}(y)=f_{1}\left(y-x_{2}\right)\left|\frac{d x}{d_{y}}\right|=\epsilon^{-\left(y-x_{2}\right)} $ (e) none of these

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(Figure 1) is the energy bar chart for a firefighter sliding down a fire pole from the second floor to the ground. Let the system consist of the firefighter, the pole, and the earth. E (J) 4 Part A What is the bar height of $U_{gf}$? Express your answer in joules as an integer. $U_{gf} =$ 2 ? ? $K_i + U_{gi} = K_f + U_{gf} + \Delta E_{th}$ Part B What is the bar height of $K_f$? Express your answer in joules as an integer. $K_f = $

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Crime prevention/reduction interventions based on differential association and social learning theory often attempt to ______. cure biological or psychological abnormalities in individuals change socially disorganized communities with socially well-organized communities improve children’s attachment to their parents remove offenders from settings that encourage crime and place into settings that provide prosocial reinforcement

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All of the following are limitations to the Uniform Crime Reports (UCR) EXCEPT for ________. ? It follows the hierarchy rule. ? It does not include information on attempted crime events. ? It does not include demographic variables. ? It only includes crimes reported to the police.

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The value of ?H° for the reaction below is -1107 kJ/mol: Ba (s) + 1/2 O2 (g) ? BaO (s) How many kJ of heat are released when 34.33 g of Ba (s) reacts completely with oxygen to form BaO (s)?

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Find X and Y X 30° 60° 700 lbs X = 305 lbs. and Y = 395 lbs. X = 350 lbs. and Y = 606 lbs. X = 606 lbs. and Y = 350 lbs. X = 395 lbs. and Y = 305 lbs. Y

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4. Find all eigenvalues of $A = \begin{bmatrix} a & b \\ b & a \end{bmatrix}$, where $a$ and $b$ are arbitrary constants. 5. Consider the matrix $A = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ k & 3 & 0 \end{bmatrix}$, where $k$ is an arbitrary constant. For which values of $k$ does $A$ have three distinct eigenvalues? What happens in the other cases?

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Select the correct answer. Molly is making a quilt for her mother. The quilt will have several designs. One of

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martin f.