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Question 3 (10 point) The error in the length of a part (absolute value of the...
Please show solutions for a to e 21. The error in the length of a part...
Please show solutions for a to e
21. The error in the length of a part (absolute value of the difference between the actual length and the target length), in mm, is a random variable with probability density function f(x) = ( 12(x2-X3 otherwise a. What is the probability that the error is less than 0.2 mm? b. Find the mean error. c. Find the variance of the error. d. Find the cumulative distribution function of the érror. e. The...
The diameter of a rivet (in mm) is a random variable with probability density function ?(?)...
The diameter of a rivet (in mm) is a random variable with probability density function ?(?) = { 3 4 (? − 9)(11 − ?) 9 < ? ≤ 11 0 ??ℎ?????? } a. find the cumulative distribution function of the diameter b. the specification of the diameter is 9.4 to 10.2. what is the probability the specification is met
Part 2. Random Variables 4. Two independent random variables Xand y are given with their distribution laws 0.3 0.7 0.8...
Part 2. Random Variables 4. Two independent random variables Xand y are given with their distribution laws 0.3 0.7 0.8 0.2 Pi Find the distribution law and variance for the random variable V-3XY 5. There are 7 white balls and 3 red balls in a box. Balls are taken from the box without return at randomm until one white ball is taken. Construct the distribution law for the number of taken balls. 6. Let X be a continuous random variable...
9.) Suppose that X is a continuous random variable with density C(1- if r [0,1 0...
9.) Suppose that X is a continuous random variable with density C(1- if r [0,1 0 ¡f x < 0 or x > 1. (a) Find C so that px is a probability density function (b) Find the cumulative distribution of X (c) Calculate the probability that X є (0.1,0.9). (d) Calculate the mean and the variance of X 10.) Suppose that X is a continuous random variable with cumulative distribution function Fx()- arctan()+ (a) Find the probability density function...
Question 1 A continuous random variable X which represents the amount of sugar (in kg) used...
Question 1 A continuous random variable X which represents the amount of sugar (in kg) used by a family per week, has the probability density function c(x-102-x) 1sxs2 ; otherwise (0) (ii) (ii) Determine the value of c. Obtain cumulative distribution function Find P(X < 1.2). Consider the following cumulative distribution function for X. 06 0.8 1.0 Fx) 0.9 (i) Determine the probability distribution. (ii) Find P(X 1). (ii) Find P(OX5) Question 3 Consider the following pdf otherwise (i) (ii)...
Suppose that X is a continuous random variable with density pX(x) = ( Cx(1 − x)...
Suppose that X is a continuous random variable with density
pX(x) = ( Cx(1 − x) if x ∈ [0, 1] 0 if x < 0 or x > 1.
(a) Find C so that pX is a probability density function.
(b) Find the cumulative distribution of X.
(c) Calculate the probability that X ∈ (0.1, 0.9).
(d) Calculate the mean and the variance of X.
9.) Suppose that X is a continuous random variable with density C(1x) if E...
(15 points) A manufacturer is studying the length of time required by a maintenance team to...
(15 points) A manufacturer is studying the length of time required by a maintenance team to respond to reported failure of a specific machine in the plant. The plant manager wants to know the percentage of repair calls answered within 10 minutes. 2. The response time, X, measured in minutes is known to have an exponential distribution. For the exponential distribution, as λ increases what happens to the mean and variance of the distribution? 4 points) Draw a sketch of...
. 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
2.5.12. The length of time that an individual talks on a long-distance telephone call has been...
2.5.12. The length of time that an individual talks on a long-distance telephone call has been found to be of a random nature. Let X be the length of the talk; assume it to be a continuous random variable with probability density function given by 0, elsewhere. Find (a) The value of a that makes fx) a probability density function. (b) The probability that this individual will talk (i) between 8 and 12 min, (ii) less than 8 min,i) more...
show steps, thanks The length of time that an individual talks on a long-distance telephone call...
show steps, thanks
The length of time that an individual talks on a long-distance telephone call has been found to be of a random nature. Let X be the length of the talk; assume it to be a continuous random variable with probability density function given by f(x)- 0, elsewhere Find (a) The value of a that makes f(x a probability density function. (b) The probability that this individual will talk (i) between 8 and 12 minutes, (i) less than...
Please show solutions for a to e
21. The error in the length of a part (absolute value of the difference between the actual length and the target length), in mm, is a random variable with probability density function f(x) = ( 12(x2-X3 otherwise a. What is the probability that the error is less than 0.2 mm? b. Find the mean error. c. Find the variance of the error. d. Find the cumulative distribution function of the érror. e. The...
Part 2. Random Variables 4. Two independent random variables Xand y are given with their distribution laws 0.3 0.7 0.8 0.2 Pi Find the distribution law and variance for the random variable V-3XY 5. There are 7 white balls and 3 red balls in a box. Balls are taken from the box without return at randomm until one white ball is taken. Construct the distribution law for the number of taken balls. 6. Let X be a continuous random variable...
9.) Suppose that X is a continuous random variable with density C(1- if r [0,1 0 ¡f x < 0 or x > 1. (a) Find C so that px is a probability density function (b) Find the cumulative distribution of X (c) Calculate the probability that X є (0.1,0.9). (d) Calculate the mean and the variance of X 10.) Suppose that X is a continuous random variable with cumulative distribution function Fx()- arctan()+ (a) Find the probability density function...
Question 1 A continuous random variable X which represents the amount of sugar (in kg) used by a family per week, has the probability density function c(x-102-x) 1sxs2 ; otherwise (0) (ii) (ii) Determine the value of c. Obtain cumulative distribution function Find P(X < 1.2). Consider the following cumulative distribution function for X. 06 0.8 1.0 Fx) 0.9 (i) Determine the probability distribution. (ii) Find P(X 1). (ii) Find P(OX5) Question 3 Consider the following pdf otherwise (i) (ii)...
Suppose that X is a continuous random variable with density
pX(x) = ( Cx(1 − x) if x ∈ [0, 1] 0 if x < 0 or x > 1.
(a) Find C so that pX is a probability density function.
(b) Find the cumulative distribution of X.
(c) Calculate the probability that X ∈ (0.1, 0.9).
(d) Calculate the mean and the variance of X.
9.) Suppose that X is a continuous random variable with density C(1x) if E...
(15 points) A manufacturer is studying the length of time required by a maintenance team to respond to reported failure of a specific machine in the plant. The plant manager wants to know the percentage of repair calls answered within 10 minutes. 2. The response time, X, measured in minutes is known to have an exponential distribution. For the exponential distribution, as λ increases what happens to the mean and variance of the distribution? 4 points) Draw a sketch of...
. 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
2.5.12. The length of time that an individual talks on a long-distance telephone call has been found to be of a random nature. Let X be the length of the talk; assume it to be a continuous random variable with probability density function given by 0, elsewhere. Find (a) The value of a that makes fx) a probability density function. (b) The probability that this individual will talk (i) between 8 and 12 min, (ii) less than 8 min,i) more...
show steps, thanks
The length of time that an individual talks on a long-distance telephone call has been found to be of a random nature. Let X be the length of the talk; assume it to be a continuous random variable with probability density function given by f(x)- 0, elsewhere Find (a) The value of a that makes f(x a probability density function. (b) The probability that this individual will talk (i) between 8 and 12 minutes, (i) less than...
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