Applied Statistics and Probability for Engineers 6th Edition solutions

Applied Statistics and Probability for Engineers 6
Suppose that \(f(x)=e^{-*}\) for 0 < x. Determine the following: (a) \(P(1<X)\) (b) \(P(1<X<2.5)\) (c) \(P(X=3)\) (d) \(P(X<4)\) (e) \(P(3 \leq X)\) (f) x such that \(P(x<X)=0.10\) (g) x such that \(P(X \leq x)=0.10\)(P(X \leq x)=0.10\) Equa

Applied Statistics and Probability for Engineers 6
Suppose that \(f(x)=3\left(8 x-x^{2}\right) / 256\) < x < 8. Determine the following: (a) \(P(X<2)\) (b) \(P(X<9)\) (c) \(P(2<X<4)\) (d) \(P(X>6)\) (e) x such that P(X < x) = 0.95 Equation transcription: Text transcription: f(x)=3(8 x-x^{

Applied Statistics and Probability for Engineers 6
Suppose that \(f(x)=0.5\) cos x for ? \(\pi / 2<x<\pi / 2\). Determine the following: (a) \(P(X<0)\) (b) \(P(X<-\pi / 4)\) (c) \(P(-\pi / 4<X<\pi / 4)\) (d) \(P(X>-\pi / 4)\) (e) x such that \(P(X<x)=0.95\) Equation transcription: Text transcri

Applied Statistics and Probability for Engineers 6
The diameter of a particle of contamination (in micrometers) is modeled with the probability density function \(f(x)=2 x^{3}\) for x > 1. Determine the following: (a) \(P(X)<2)\) (b) \(P(X>5)\) (c) \(P(4<X<8)\) (d) \(P(X<4\) or \(x>8 \text { ) }\) (e) x suc

Applied Statistics and Probability for Engineers 6
Suppose that \(f(x)=x / 8\) for \(3<x<5\). Determine the following probabilities: (a) \(P(X<4)\) (b) \(P(X>3.5)\) (c) \(P(4<X<5)\) (d) \(P(X<4.5)\) (e) \(P(X<3.5 \text { or } X>4.5)\)

Applied Statistics and Probability for Engineers 6
Suppose that \(f(x)=e^{-(x-4)}\) for \(4<x\). Determine the following: (a) \(P(1<X)\) (b) \(P(2 \leq X<5)\) (c) \(P(5<X)\) (d) \(P(8<X<12)\) (e) x such that \(P(X<x)=0.90\)

Applied Statistics and Probability for Engineers 6
Suppose that \(f(x)=1.5 x^{2}\) for \(-1<x<1\). Determine the following: (a) \(P(0<X)\) (b) \(P(0.5<X)\) (c) \(P(-0.5 \leq X \leq 0.5)\) (d) \(P(X<-2)\) (e) \(P(X<0\) or \(X>-0.5)\) (f) x such that \(P(x<X)=0.05\). Equation transcription:

Applied Statistics and Probability for Engineers 6
Problem 8E The probability density function of the time to failure of an electronic component in a copier (in hours) is f (x) = e?x /1000/1000 for x > 0??Determine the probability that (a) A component lasts more than 3000 hours before failure. (b) A component fails in the interval from 1000 to 2000 h

Applied Statistics and Probability for Engineers 6
Problem 9E The probability density function of the net weight in pounds of a packaged chemical herbicide is f (x) = 2.0 for 49.75 < x < 50.25 pounds. (a) Determine the probability that a package weighs more than 50 pounds. (b) How much chemical is contained in 90% of all packages?

Applied Statistics and Probability for Engineers 6
The probability density function of the length of a cutting blade is \(f(x)=1.25\) for \(74.6<x<75.4\) millimeters. Determine the following: (a) \(P(X<74.8)\) (b) \(P(X<74.8\) or \(X>75.2)\) (c) If the specifications for this process are from 74.7 to 75.3 millimeters, what proportion of b

Applied Statistics and Probability for Engineers 6
Problem 11E The probability density function of the length of a metal rod is f (x) = 2 for 2.3 < x < 2.8 meters. (a) If the specifications for this process are from 2.25 to 2.75 meters, what proportion of rods fail to meet the specifications? (b) Assume that the probability density function is f (x)

Applied Statistics and Probability for Engineers 6
An article in Electric Power Systems Research [Modeling Real-Time Balancing Power Demands in Wind Power Systems Using Stochastic Differential Equations (2010, Vol. 80(8), pp. 966974)] considered a new probabilistic model to balance power demand with large amounts of wind power. In this model, the pow

Applied Statistics and Probability for Engineers 6
A test instrument needs to be calibrated periodically to prevent measurement errors. After some time of use without calibration, it is known that the probability density function of the measurement error is \(f(x)=1-0.5 x\) for \(0<x<2\) millimeters. (a) If the measurement error within 0.5 millimet

Applied Statistics and Probability for Engineers 6
The distribution of X is approximated with a triangular probability density function \(f(x)=0.025 x-0.0375\) for \(30<x<50\) and \(f(x)=-0.025 x+0.0875\) for \(50<x<70\). Determine the following: (a) \(P(X \leq 40)\) (b) \(P(40<X \leq 60)\) (c) Value x exceeded with probability 0.

Applied Statistics and Probability for Engineers 6
The waiting time for service at a hospital emergency department (in hours) follows a distribution with probability density function \(f(x)=0.5 \exp (-0.5 x)\) for \(0<x\). Determine the following: (a) \(P(X<0.5)\) (b) \(P(X>2)\) (c) Value x (in hours) exceeded with probability 0.0

Applied Statistics and Probability for Engineers 6
Problem 16E If X is a continuous random variable, argue that P(x1 ? X ? x2 ) = P(x1 < X ? x2 )= P(x1 ? X < x2 )= P(x1 < X < x2 ).