Information for Problems 7 - 10: The diameter, x (in micrometers), of a particle of contamination...
f X = for X > The diameter of a particle of contamination in micrometers) is modeled with the probability density function places) (a) P(X <7) (b) P(X > 10) Determine the following (round all of your answers to 3 decimal P7X11) (d) P(X 7 or X > 11) (e) Determine X such that P(X x) = 0.99
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
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)...
4 3.29 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 13-4, 171 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 4 micrometers? (d) Find & {x}
help 4). 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 2x1 f)to.l otherwtse (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 4 micrometers?
Question 4 (14 points) Particles are a major component of air pollution in many areas. It is of interest to study the sizes of contaminating particles. Let X represent the diameter, in micrometers, of a randomly chosen particle. Assume that in a certain area, the probability density function of X is inversely proportional to the volume of the particle; that is, assume that r 21 where c is a constant. a. Find the value of c so that f(x) is...
part a, b and c please Problem 4. (15 points) The probabiälity density function of X, the lifetime of a lamp (meured in i hours), Is given 10 0, s 10 (a) Find P(x>20) 3 b) What is the cumulative distribution fpaction of (e) What is the probability that, of 3 of these lampe, at keast 2 will function for at least 15 hours? Assume that the 3 lamps function/fail independent of each other 7 Problem 4. (15 points) The...
Answer Q4 only. 2. An important factor in solid missile fuel is the particle size distribution. Significant pro- blems 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 (5x-6, X >1, elsewhere. Find F(x). 3. Use the same probability distribution as in Question 2. What is the probability that a random particle from the manufactured fuel exceeds 3 micrometers? (You could...
Let X be the lifetime of a certain type of electronic device (measured in hours). The probability density function of X is f(x) =10/x^2 , x > c 0, x ≤ c (a) Find the value of c that makes f(x) a legitimate pdf of X. (b) Compute P(X < 20).