Prob-2 The diameter of metal cylinder has a probability density function of f(x)=1.5-6(x-50)2 [mm] 500 metal...
eeR papers as stableah No Question to instructor! If you belive t statement; use your assumption to solve the problem. Breaking the e Prob-1 Probability that cars have been assembled in a particular plant as follows: Pl plant I )-20% , P(plam2)-24% , P(plant3)-25% , P(plant4)-31 % Total number of cars manufactuted by all plants: 1.2 million/year Number of cars of no warranty claims manufactured by plantl: 223200/year ty claim rate of the cars assembeled in plantl? Ans: Prob-2 The...
3.5 A compound thin cylinder has a common diameter of 100 mm and the inner cylinder has a thickness of 2,5 mm. The radial pressure between the two cylinders is 200 kPa and the difference between the two common diameters before shrinkage was 4,305 x 10-3 mm. Determine the (a) thickness of the outer cylinder; (b) resultant hoop stresses in both cylinders if the compound cylinder is subjected to an internal pressure of 180 kPa (E 200 GPa). 2 mm]...
1) The probability density function of the diameter (in micrometers) of a particular type of contaminant particle can be modeled by f(x) = (x3 Exp(-x/2)]/96, x 20 a) Plot the pdf and the CDF of these diameters b) Compute E(Diameter) y Var(Diameter) c) Compute Pr(Diameter > 4), Pr(Diameter > 8), and Pr(Diameter > 12), d) Assume that the following random sample of 100 diameters of these particles has been taken. What is the probability that sample average if greater than...
1. (50 points) For the probability density function shown below (a) Determine the expected value of X. (b) What is the probability that X is less than 2? (c) What is the probability that X is between 1 and 2? fx(x) _ 2 3 2. (50 points) Suppose that the diameter X of a certain type of weld is uniformly distributed between 0.2 mm and 4.2 mm. (a) Determine and plot the PDF and CDF of X. (b) What is...
3) The continuous random variable X has the probability density function, ), 2 3x3 f(x) = { a, 35x55 2 - bx, 5 < x < 6 elsewere 10 i)Find the value of a and b and hence, sketch f(x) ii) Find the cumulative distribution function, f(x) and sketch it.
Member (1) is a solid 50 mm diameter cylinder made from magnesium. The modulus of elasticity is 44.7 GPa and the thermal coefficient of expansion is 26 x 106/°C. The cylinder is placed in a clamp when the temperature is 20℃ Two stainless steel carriage bolts (2) hold the cylinder snug with negligible force against the rigid jaws of the clamp. Each bolt has a diameter of 10 mm, modulus of elasticity of 193 GPa, and a coefficient of thermal...
(7) Let X1,Xn are i.i.d. random variables, each with probability distribution F and prob- ability density function f. Define U=max{Xi , . . . , X,.), V=min(X1, ,X,). (a) Find the distribution function and the density function of U and of V (b) Show that the joint density function of U and V is fe,y(u, u)= n(n-1)/(u)/(v)[F(v)-F(u)]n-1, ifu < u. (7) Let X1,Xn are i.i.d. random variables, each with probability distribution F and prob- ability density function f. Define U=max{Xi...
A cylindrical piece of steel has a diameter of 50 mm and a length of 200 mm. Steel has a density of 7200 kg/m3 a) (3 points) Determine the mass of this piece in kg. 1. b) (3 points) If a 10 mm diameter opening is drilled through the entire length of this cylinder and that portion removed, what is the new mass of this piece? c) (4 points) The 10 mm diameter piece is pulled with a force of...
Suppose that X has the probability density function f(x) = { 2x 0 < x < 1 0 otherwise Which of the following is the moment generating function of X? 2 et t 2 et t2 2 t2 O t2 2 eet t 2 ett t2 t e eut-1 t
2. The random variable X has probability density function f given by f(x) 0 otherwise. (a) Is X continuous or discrete? Explain. (b) Calculate E(X). (c) Calculate Var(2X 9).