(2)

5.(15%) Let X and Y be two independent random variables that follow a Poisson distribution with rate parameter θ and λ, respectively, i.e., X ~ Poisson(θ) and Y ~ Poisson(λ), Show that the distribution of X/(X+Y) is binomial with success probabilityθ/(θ+λ). Note: the probability density function of a Poisson distribution with rate parameter y is

(1)Find E[Y], Var[Y], and Cov(X, Y). (15%)

(2)Prove that Y/X and Xare independent. (10%)

1. Determine the mg/L of O2 required for a BOD test if 0.1 mmol of urea, (NH2)2CO, is completely oxidized into CO2, and water in a 50 ml sample. (20 points)

2. A stack gas contains carbon monoxide (CO) at a concentration of 10 % by volume. What is the concentration of CO in ug/m3? (assuming 25℃ and I atmosphere pressure) (20 points)

3. Express 10 mg/L of as CaCO3. (Mg=24, Ca=40, C=12, O=16) (20 points)

4. A stack emission has the following characteristics: 90 % SO2, 10 % N2 and no particulates. What treatment device would you suggest and why? (20 points)

5. A one liter cylinder is used to measure the settleability of 0.5 % suspended solids sludge. After 30 min the settle sludge occupy 600 ml. Calculate the Sludge Volume Index (SVI)?? (20 points)

1.One hundred moles per minute of a binary mixture of 50% A and 50% B are separated in a two-stage (serial) process. In the first stage, the liquid and vapor flow rates exiting from the stage are each 50 mol/min. The liquid stream is then passed into a second separator that operates at the same temperature as the first stage. The temperature is the same for each stage, and at that temperature, the vapor pressure of A is 10 kPa and the vapor pressure of B is 100 kPa. Treat the liquids and vapors as ideal. Calculate the compositions of the vapor and liquid streams, and the pressure in the first stage. (30%)

(1) Derive an expression relating, to measurable properties. (10%)

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