Based on the standard analytical practice during a titration of taking pH-volume measurements every 0.3 pH units, how many measurements should you take between the addition of 5 mL and 7.5 mL of titrant, (a) in the titration of a 10-mL aliquot of standard 0.1500 M TRIS base (pKb = 1.2 X 10-6) (in beaker) with 0.1000 M HCl (in buret). (b) in the titration of a 10-mL aliquot of 0.1500 M NaOH (in buert) with standard 0.1000 M HCl (in buret).

Hints: To solve these questions, it may be helpful to draw a diagram of the titration set up. Before starting, reason out whether the pH will increase or decrease with the addition of titrant. You need to calculate the pH at the 5 and 7.5 mL points in each of the two titrations. Because HCl and NaOH are a strong acid and base respectively, they dissociate completely and the pH of the solution is dependent only on the excess acid or base in the beaker at that point in the titration.

Let X denote a random variable that follows a binomial distribution with parameters n=5, p=0.3, and Y denote a random variable that has a Poisson distribution with parameter λ = 6. Additionally, assume that X and Y are independent random variables.

1. What are the possible values for (X, Y ) pairs.

2. Derive the joint probability distribution function for X and Y. Make sure to explain your steps.

3. Using the joint pdf function of X and Y, form the summation /integration (whichever is relevant) that gives the expected value for X4 + Y + 7.

4. Using the joint pdf function of X and Y, set up the summation /integration (whichever is relevant) that gives the expected value for X, and COMPUTE its value.

Let X denote a random variable that follows a binomial distribution with parameters n=5, p=0.3, and Y denote a random variable that has a Poisson distribution with parameter λ = 6. Additionally, assume that X and Y are independent random variables.

1. What are the possible values for (X, Y ) pairs.

2. Derive the joint probability distribution function for X and Y. Make sure to explain your steps.

3. Using the joint pdf function of X and Y, form the summation /integration (whichever is relevant) that gives the expected value for X^4 + Y + 7.

4. Using the joint pdf function of X and Y, set up the summation /integration (whichever is relevant) that gives the expected value for X, and COMPUTE its value.

Consider the following scenario analysis:

Assume a portfolio with weights of 0.60 in stocks and 0.40 in bonds.

1. What is the rate of return on the portfolio in each scenario? (Enter your answer as a percent rounded to 1 decimal place.)

b. What are the expected rate of return and standard deviation of the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

c. Would you prefer to invest in the portfolio, in stocks only, or in bonds only? Explain the benefit of diversification.

Use 5 months moving average and exponential smoothing method (using alpha=0.3) on the following sale of Maggi. You are supposed to forecast the sale of Maggi in the 13^th Month. Compare whether there is any difference in forecast based on two methods and Comment.

A pitched baseball (m=0.3 kg) reaches a catcher’s glove travelling at a velocity of 28 m/s. Calculate the ball’s: A) momentum, B) kinetic energy. How much impulse is required to catch the ball? If the hand moves backward 32cm while the person is catching it, what is the average force applied to the ball? How much time will it take before the ball stops? What is the average power of this contact?

The variation of the spectral transmissivity of a 0.6cm thick glass window is 0.92 in the wavelength range from 0.3-3micrometer. Determine the average transmissvity of this window for solar radiation at T=5800K. Also, determine the amount of solar radiation transmitted through the window for incident solar radiation of 650W/m².

2. Let X be a continuous random variable with PDF ?fx(x)= cx(1 − x), 0 < x < 1,

0 elsewhere.

(a) Find the value of c such that fX(x) is indeed a PDF.

(b) Find P(−0.5 < X < 0.3).

(c) Find the median of X.

describe how to make one liter of the following solution: 0.3 M mannitol (FW=182), 0.02 M KPO4, 0.01 M KCl, 0.005 M MgCl2. You have the following stocks... 1 M KPO4, 1 M KCl, 1 M MgCl2.

A capacitor is connected to a battery and placed in a magnetic field (-z direction) to form a velocity selector. A charge moving at 3,479.6 m/s is not deflected by the velocity selector. If the voltage of the battery is 7 volts and the distance between the sheets is 0.3 meters, what is the amount of the magnetic field in milli-Tesla?