1. Determine cumulative distribution function for the distribution of the diameter of a particle of contamination...
1. Determine cumulative distribution function for the distribution of the diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x) = 2/x3 for x > 1:
a. P(X < 2)
b. P(X > 5)
c. P(4 < X < 8)
d. P(X < 4 or X > 8)
e. x such that P(X < x) = 0.95
2.Suppose that the cumulative distribution function of the random variable X is
Determine the following:
a. P(X < 2.8)
b.P(X > 1.5)
c. P(X < −2)
d. P(X > 6)
Homework Answers
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1. Determine cumulative distribution function
for the distribution of the diameter of a particle of contamination...
f X = for X > The diameter of a particle of contamination in micrometers) is...
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
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)
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
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...
1. You are given a function (a) Show that F(x) is a cumulative distribution function of...
1. You are given a function (a) Show that F(x) is a cumulative distribution function of a certain random variable X on [3, 4]. (b) function associated with F(x Find the probability density (c) Calculate the probability that X is no more than 3.5, given that it exceeds 3.2. (d) Determine the expected value of X.
Question 3: Let X be a continuous random variable with cumulative distribution function FX (x) =...
Question 3: Let X be a continuous random variable with
cumulative distribution function FX (x) = P (X ≤ x). Let Y = FX
(x). Find the probability density function and the cumulative
distribution function of Y .
Question 3: Let X be a continuous random variable with cumulative distribution function FX(x) = P(X-x). Let Y = FX (x). Find the probability density function and the cumulative distribution function of Y
. The average monthly rainfall (AMR) in inches is a random variable with the cumulative distribution...
. The average monthly rainfall (AMR) in inches is a random
variable with the cumulative distribution function (cdf):\
a. Determine the probability that the AMR is less than 1.5
inches.
b. Determine the probability the AMR is between 1.5 and 2
inches.
c. What is the median AMR? d. Determine the equation describing
the probability density function (pdf), f(x)
4 F(x) = .16, otherwise 1.2 1.0 0.8 0.4 0.2 0.0 97.5 98 98.5 99.5 100 100.5
Define the random variable Y = -2X. Determine the cumulative distribution function (CDF) of Y ....
Define the random variable Y = -2X. Determine the cumulative
distribution function (CDF) of Y . Make sure to completely specify
this function. Explain.
Consider a random variable X with the following probability density function (PDF): s 2+2 if –2 < x < 2, fx(x) = { 0 otherwise. This random variable X is used in parts a, b, and c of this problem.
A mixed random variable X has the cumulative distribution function e+1 (a) Find the probability density...
A mixed random variable X has the cumulative distribution function e+1 (a) Find the probability density function. (b) Find P(0< X < 1).
12. (15 points) Let X be a continuous random variable with cumulative distribution function **- F()...
12. (15 points) Let X be a continuous random variable with cumulative distribution function **- F() = 0, <a Inx, a < x <b 1, b<a (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
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
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)
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...
1. You are given a function (a) Show that F(x) is a cumulative distribution function of a certain random variable X on [3, 4]. (b) function associated with F(x Find the probability density (c) Calculate the probability that X is no more than 3.5, given that it exceeds 3.2. (d) Determine the expected value of X.
Question 3: Let X be a continuous random variable with
cumulative distribution function FX (x) = P (X ≤ x). Let Y = FX
(x). Find the probability density function and the cumulative
distribution function of Y .
Question 3: Let X be a continuous random variable with cumulative distribution function FX(x) = P(X-x). Let Y = FX (x). Find the probability density function and the cumulative distribution function of Y
. The average monthly rainfall (AMR) in inches is a random
variable with the cumulative distribution function (cdf):\
a. Determine the probability that the AMR is less than 1.5
inches.
b. Determine the probability the AMR is between 1.5 and 2
inches.
c. What is the median AMR? d. Determine the equation describing
the probability density function (pdf), f(x)
4 F(x) = .16, otherwise 1.2 1.0 0.8 0.4 0.2 0.0 97.5 98 98.5 99.5 100 100.5
Define the random variable Y = -2X. Determine the cumulative
distribution function (CDF) of Y . Make sure to completely specify
this function. Explain.
Consider a random variable X with the following probability density function (PDF): s 2+2 if –2 < x < 2, fx(x) = { 0 otherwise. This random variable X is used in parts a, b, and c of this problem.
A mixed random variable X has the cumulative distribution function e+1 (a) Find the probability density function. (b) Find P(0< X < 1).
12. (15 points) Let X be a continuous random variable with cumulative distribution function **- F() = 0, <a Inx, a < x <b 1, b<a (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
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