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Question 6 The diameter of a particle of contamination (in micrometers) is modeled with the probability...
Question 6 The diameter of a particle of contamination (in micrometers) is modeled with the probability density function for x>1. Determine the following (round all of your answers to 3 decimal places): (a) P(X < 7) (b) P(X > 10) (c) P(6< X < 10) C (d) P(X < 6 or X > 10) (e) Determine X such that P(X<X) = 0.85. Question Attempts: 0 of 3 used SAVE FOR LATER SUBMIT ANSWER
Information for Problems 7 - 10: The diameter, x (in micrometers), of a particle of contamination...
Information for Problems 7 - 10: The diameter, x (in micrometers), of a particle of contamination has the following probability density function (pdf): f(x)-C(e0.3*) for x 22 7. Find the value of C that makes this a legitimate probability density function. (3 points) 8. Find the cumulative distribution function, F(x). (4 points) 9. Find PCX s 3) and P(X 2 3). (4 points) 10. Find x such that P(X x) 0.10. (4 points)
1) The probability density function of the diameter (in micrometers) of a particular type of contaminant...
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...
An important factor in solid missile fuel is the particle size distribution. Significant problems occur if...
An important factor in solid missile fuel is the particle size distribution. Significant problems occur if the particle sizes are too large. From production data in the past, it has been determined that the particle size (in micrometers) distribution is characterized by the following function. f(x) = 3x-4, x>1 10, elsewhere (a) Verify that this is a valid density function. (b) Evaluate F(x). (c) What is the probability that a random particle from the manufactured fuel exceeds 9 micrometers? (a)...
Determine the value of such that the function f (x, y) = cxy for 0<x<3 and...
Determine the value of such that the function f (x, y) = cxy for 0<x<3 and 0 <y<3 satisfies the properties of a joint probability density function. Determine the following. Round your answers to four decimal places (e.g. 98.7654). 1.0994 P&<2,Y<3) 7.4444 P(X<2.0) 21:1878 Pu<Y<1,7) 12489 P(X>1.8,1 <Y<2.5) 7:3733 EX) P(X < 0,8< 4)
Question 12: Let X and Y have the joint probability density function Find P(X>Y), P(X Y...
Question 12: Let X and Y have the joint probability density function Find P(X>Y), P(X Y <1), and P(X < 0.5)
Suppose that f(x) - or 0<X<8 256 Determine the following probabilities. Round your answers to 3...
Suppose that f(x) - or 0<X<8 256 Determine the following probabilities. Round your answers to 3 decimal places (e.g. 98.765) (a) P(X < 2)=7456 (b) P(X< 9) = (d) P(X > 5)- 316 (e) Determine such that P(x x)-0.90 X6.302
1. Let X be a continuous random variable with probability density function f(x) = { if...
1. Let X be a continuous random variable with probability density function f(x) = { if x > 2 otherwise 0 Check that f(-x) is indeed a probability density function. Find P(X > 5) and E[X]. 2. Let X be a continuous random variable with probability density function f(x) = = { SE otherwise where c is a constant. Find c, and E[X].
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise....
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise. (a) Find c (b) Find the distribution function Fx) (c) Compute P(l <X<3)
Suppose a joint probability density function for two variables X and Y is given as follows:...
Suppose a joint probability density function for two variables X and Y is given as follows: {24x0, if 0 < x < 1,0 < y < 1 f(x, y) = otherwise Please find the probability p (w > 1) =? 3
Question 6 The diameter of a particle of contamination (in micrometers) is modeled with the probability density function for x>1. Determine the following (round all of your answers to 3 decimal places): (a) P(X < 7) (b) P(X > 10) (c) P(6< X < 10) C (d) P(X < 6 or X > 10) (e) Determine X such that P(X<X) = 0.85. Question Attempts: 0 of 3 used SAVE FOR LATER SUBMIT ANSWER
Information for Problems 7 - 10: The diameter, x (in micrometers), of a particle of contamination has the following probability density function (pdf): f(x)-C(e0.3*) for x 22 7. Find the value of C that makes this a legitimate probability density function. (3 points) 8. Find the cumulative distribution function, F(x). (4 points) 9. Find PCX s 3) and P(X 2 3). (4 points) 10. Find x such that P(X x) 0.10. (4 points)
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...
An important factor in solid missile fuel is the particle size distribution. Significant problems occur if the particle sizes are too large. From production data in the past, it has been determined that the particle size (in micrometers) distribution is characterized by the following function. f(x) = 3x-4, x>1 10, elsewhere (a) Verify that this is a valid density function. (b) Evaluate F(x). (c) What is the probability that a random particle from the manufactured fuel exceeds 9 micrometers? (a)...
Determine the value of such that the function f (x, y) = cxy for 0<x<3 and 0 <y<3 satisfies the properties of a joint probability density function. Determine the following. Round your answers to four decimal places (e.g. 98.7654). 1.0994 P&<2,Y<3) 7.4444 P(X<2.0) 21:1878 Pu<Y<1,7) 12489 P(X>1.8,1 <Y<2.5) 7:3733 EX) P(X < 0,8< 4)
Question 12: Let X and Y have the joint probability density function Find P(X>Y), P(X Y <1), and P(X < 0.5)
Suppose that f(x) - or 0<X<8 256 Determine the following probabilities. Round your answers to 3 decimal places (e.g. 98.765) (a) P(X < 2)=7456 (b) P(X< 9) = (d) P(X > 5)- 316 (e) Determine such that P(x x)-0.90 X6.302
1. Let X be a continuous random variable with probability density function f(x) = { if x > 2 otherwise 0 Check that f(-x) is indeed a probability density function. Find P(X > 5) and E[X]. 2. Let X be a continuous random variable with probability density function f(x) = = { SE otherwise where c is a constant. Find c, and E[X].
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise. (a) Find c (b) Find the distribution function Fx) (c) Compute P(l <X<3)
Suppose a joint probability density function for two variables X and Y is given as follows: {24x0, if 0 < x < 1,0 < y < 1 f(x, y) = otherwise Please find the probability p (w > 1) =? 3
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