Suppose X~ Exponential (X). What is the distribution of cX for a constant e > 0? Justify your answer.

Obtain relations for the characteristic lengths of a large plane wall of thickness 2L, a very long cylinder of radius ro, and a sphere of radius ro.

Show that when 1(x,t) and 2(x,t) are solutions to the time-dependent Schrödinger equation and A, B are numbers then a function (x,t) that is a superposition of these functions is also a solution: (x,t)=A1(x,t)+B1(x,t).

Evaluate the function f(x) = 0.15x^3 − 3.18x^2 − 2.4x+ 17.1 for x=0.14, where, xis rounded. Compute the absolute error and error bound.

For T = 0.3 sec, write the element of the discrete sequence corresponding to the function f(t) = 5t with k = 18. Provide your answer in seconds to the nearest first decimal place. Pay attention to the numbers given

Use the measured values of V1 and V2 to calculate a predicted value for Vcombo. Also, calculate the %-difference.

Compute |(x,t)|2 for the function (x,t)=(x)sint, where is a real constant.

Use the fact that at the critical point the first and second partial derivatives of P with respect to Vm at constant T are zero (∂P/∂Vm=∂2P/∂V2m=0) to derive the expressions for the Van der Waals constants in terms of critical parameters. Show full and complete procedure, do not skip any step

can u solve this 7b?

Let p(x, y) be the joint probability distribution of the two random variables X and Y. Define the conditional entropy H(X | Y ) in terms of the joint distribution and associated conditional probabilities.