Use part (a) to show that X and Y are independent.

1.  Refer to Exercise 30. An equation to predict the ductility of a titanium weld is Y = 7.84C + 11.44N + O − 1.58Fe, where Y is the oxygen equivalence used to predict ductility, and C, N, O, and Fe are the amounts of carbon, nitrogen, oxygen, and iron, respectively, in weight percent, in the weld. Using the means, standard deviations, and correlations presented in Exercise 30, find µY and σY


2.  Let X and Y be jointly continuous with joint probability density function f(x, y) and marginal densities fX (x) and fY (y). Suppose that f(x, y) = g(x)h(y) where g(x) is a function of x alone, h(y) is a function of y alone, and both g(x) and h(y) are nonnegative.

a.  Show that there exists a positive constant c such that fX (x) = cg(x) and fY (y) = (1/c)h(y).

b.   Use part (a) to show that X and Y are independent.


find the cost of your paper

Determine the outlet concentration x1 in the water solution and in the trichloroethane solution using an analytical equation.

Predicting Extraction for an Existing Tower with a Given Number of Steps. An existing tower contains 5.0 theoretical steps. It is desired to predict its performance under the following conditions….

Calculate the minimum solvent that can be used. [Hint: In this case, the tie line through the feed L0 represents the condition for minimum solvent flow rate.

Minimum Solvent and Countercurrent Extraction of Acetone. An aqueous feed solution of 1000 kg/h containing 23.5 wt % acetone and 76.5 wt % water is being extracted in a countercurrent….

Determine the break-point time, the fraction of total capacity used up to the break point, the length of the unused bed, and the saturation loading capacity of the solid.

Drying of Nitrogen and Scale-Up of a Column. Using molecular sieves, water vapor was removed from nitrogen gas in a packed bed (C1) at 28.3°C. The column height was 0.268….