An automatic machine produces on average, 10% of its components outside of the tolerance required. In a sample of 10 components from this machine, determine the probability of having two components outside of the tolerance required by assuming a binomial distribution.

The probability density function of the discrete random variable X is given as follows. px (0) = 4c, px (1) = 3c, px (2) = 2c, px(3) = c P(X > E[X]) find the probability FIND THE VARIANCE, YES(X).

For a classical ideal gas given the square root of p^2 in the amount a(mkt) then the value of a is

1- Consider the measurement of pressure in a gas through measurement of its temperature T and densityp Let the uncertainties of T and p be ôT and op where p is determined from the ideal gas p=pRT. Derive an expression of uncertainty (error) in P and determine ôP/P. Suppose the uncertainty in op is 1% and in ôT is 2° at T=27°.

The headway h is the average time between vehicles. On a highway carrying an average of 500 vehicles per hour, the probability P that the headway is at least t seconds is given by the following formula.t P = 0.87 (a) What is the limiting value of P? Explain what this means in practical terms. This means that the probability of finding very large headways is small (b) The headway can be calculated as the quotient of the spacing f in feet, which is the average distance between vehicles, and the average speed v, in feet per second, of traffic. Thus, the probability that spacing is at least f feet is the same as the probability that the headway is at least f/v seconds. Use function composition to find a formula for the probability Q that the spacing is at least f feet. Note: Your formula will involve both fand v. Q = (c) If the average speed is 90 feet per second, what is the probability that the spacing between two vehicles is at least 41 feet? (Round your answer to the nearest whole…

Oshow That if The drstan ces are measur ed from the unit Planes, That fo cal lengTh of SYS hem is given by The reciero cal of The element of The system mabyi X

What is “fractional error” for the following formula? Z= 2/3 X2Y3  ,  X= 7m , Y= 4m,   σx=0.2m  ,  σy=0.1m σZ=?

The partition funetion for the ensemble characterized by constant V, E, and G = µÑ is given to a very good approximation by ø(V, E, µN)=Q(N,V,E)eBHN, where G = µN is the Gibbs energy (µ is the chemical potential and N is the average number of particles). Find an expression for the characteristic thermodynamic function for this ensemble in terms of the partition function ø(V, E, µN).

QUESTION 4 E sin () sin () sin () 3nx 2nz Consider the case of a 3-dimensional particle-in-a-box. Given: Y = 1.5 What is the size of the box along the x-dimension? 2 3 none are correct

If 4 letters are put at random into 4 envelopes, what is the probability that at least one letter gets into the correct envelope?