Let X be the number of failures for a certain machine during a
month. Its cumulative
distribution function is
What is the expected number of failures for a month?
A. 2.50 B. 3.00 C. 2.32 D. 11.94 E. none of the above
Homework Answers
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Let X be the number of failures for a certain machine during a
month. Its cumulative...
Let X be the number of failures for a certain machine during a month. Its cumulative...
Let X be the number of failures for a certain machine during a month. Its cumulative distribution function is 0 if x < 0 0.17 if 0 < x < 1 0.40 if i <r < 2 Fx (2) = { 0.59 if 2<x<3 0.72 if 3 <3 <4 0.80 if 4 <<5 1 if x>5 Compute the probability that there will be more than 3 failures during a month. A. 0.28 B. 0.72 C. 0.20 D. 0.80 E. 0.41
18. Multiple Choice Question Assume that random variable X be the excess weight of a "1000...
18. Multiple Choice Question Assume that random variable X be the excess weight of a "1000 grams" bottle of soap. Let X follows a normal distribution with variance 169 g. What sample size is required to have a level of confidence of 95% that the maximum error of the estimate of the mean of the excess weight is less than 1.5g? A. 302 B. 287 C. 289 D. 301 E. 288 0 19. Multiple Choice Question Let X be the...
(a) Find P{X=2} (b) Find P{X<2} (c) Find P{2 <= X < 2.5} The cumulative distribution...
(a) Find P{X=2}
(b) Find P{X<2}
(c) Find P{2 <= X < 2.5}
The cumulative distribution of a random variable X is given as 0 x < 0 0<x<2 4 Fx(x) = 2<x<3 4 x 3 x + 1
Below is a probability distribution for the number of failures in an elementar statistics course. X...
Below is a probability distribution for the number of failures in an elementar statistics course. X 0 1 2 3 4 P(X=x) 0.41 0.16 ? 0.07 0.16 Determine the following probabilities: a. P(X = 2) = b. P(X<2) = c. P(X<2) = d. P(X > 2) = e. P(X = 1 or X= 4) = f. P(1<x< 4) =
Random variable X has the following cumulative distribution function: 0 x〈1 0.12 1Sx <2 F(x) 0.40...
Random variable X has the following cumulative distribution function: 0 x〈1 0.12 1Sx <2 F(x) 0.40 2 x<5 0.79 5 x<9 1x29 a. Find the probability mass function of X. b. Find E[X] c. Find E[1/(2X+3)] d. Find Var[X]
(5) Let X, i = 1,...,n be iid sample from density fx(x) = f(x) e-/201(x >...
(5) Let X, i = 1,...,n be iid sample from density fx(x) = f(x) e-/201(x > 0), 4 > 0 V TO (a) Find k. (b) Find E(X). (c) Find Var(X). (d) Find the MLE for 0. (e) Find MOM estimator for A. (f) Find bias for MLE. (g) Find MSE of MLE. (h) Let Y = x, find probability density function of Y. (i) Let Y = X?, find cumulative distribution function of Y. 5
By specifying its probability function,pX, and a random variable X with cumulative distribution function:
By specifying its probability function,px, and a random variable X with cumulative distribution function:FX(t) =8>>>>>>>>><>>>>>>>>>:0; t <31=3;3t <41=2;4t <52=3;5t <61; t6Calculate Pr(3X4).
A newly installed automatic gate system was being tested to see if the number of failures...
A newly installed automatic gate system was being tested to see if the number of failures in 1,000 entry attempts was the same as the number of failures in 1,000 exit attempts. A random sample of eight delivery trucks was selected for data collection. Do these sample results show that there is a significant difference between entry and exit gate failures? Use a = 0.01. Entry failures Exit failures Truck 1 44 45 Truck 2 43 52 Truck 3 51...
About 1% of a certain type of LED diodes fails during a 24-hour test. Failures are assumed to be independent. Consider a lightstrip consisting of 10 such LED diodes. Let X be the number of LED diodes that fail during the 24-hour test. i) What distributio
About 1% of a certain type of LED diodes fails during a 24-hour test. Failures are assumed to be independent.Consider a lightstrip consisting of 10 such LED diodes.Let X be the number of LED diodes that fail during the 24-hour test.i) What distribution does X follow?ii) What is the probability that the lightstrip will burn for the full 24-hour test with no LED diodes failure?iii) What is the probability that the lightstrip will lose at least 3 LED diodes during...
The number of accidents in a month at a certain intersection, denoted by X, has been...
The number of accidents in a month at a certain intersection, denoted by X, has been found to follow the Poisson distribution with its mathematical expectation, that is, E(X), equal to 6. What is the probability that X is larger than 4 in a certain month? What is the probability that X is no more than 1 in a certain month? 1) The probability that X is larger than 4 in a certain month is: Pr(X>4)= 2) The probability that...
Let X be the number of failures for a certain machine during a month. Its cumulative distribution function is 0 if x < 0 0.17 if 0 < x < 1 0.40 if i <r < 2 Fx (2) = { 0.59 if 2<x<3 0.72 if 3 <3 <4 0.80 if 4 <<5 1 if x>5 Compute the probability that there will be more than 3 failures during a month. A. 0.28 B. 0.72 C. 0.20 D. 0.80 E. 0.41
18. Multiple Choice Question Assume that random variable X be the excess weight of a "1000 grams" bottle of soap. Let X follows a normal distribution with variance 169 g. What sample size is required to have a level of confidence of 95% that the maximum error of the estimate of the mean of the excess weight is less than 1.5g? A. 302 B. 287 C. 289 D. 301 E. 288 0 19. Multiple Choice Question Let X be the...
(a) Find P{X=2}
(b) Find P{X<2}
(c) Find P{2 <= X < 2.5}
The cumulative distribution of a random variable X is given as 0 x < 0 0<x<2 4 Fx(x) = 2<x<3 4 x 3 x + 1
Below is a probability distribution for the number of failures in an elementar statistics course. X 0 1 2 3 4 P(X=x) 0.41 0.16 ? 0.07 0.16 Determine the following probabilities: a. P(X = 2) = b. P(X<2) = c. P(X<2) = d. P(X > 2) = e. P(X = 1 or X= 4) = f. P(1<x< 4) =
Random variable X has the following cumulative distribution function: 0 x〈1 0.12 1Sx <2 F(x) 0.40 2 x<5 0.79 5 x<9 1x29 a. Find the probability mass function of X. b. Find E[X] c. Find E[1/(2X+3)] d. Find Var[X]
(5) Let X, i = 1,...,n be iid sample from density fx(x) = f(x) e-/201(x > 0), 4 > 0 V TO (a) Find k. (b) Find E(X). (c) Find Var(X). (d) Find the MLE for 0. (e) Find MOM estimator for A. (f) Find bias for MLE. (g) Find MSE of MLE. (h) Let Y = x, find probability density function of Y. (i) Let Y = X?, find cumulative distribution function of Y. 5
A newly installed automatic gate system was being tested to see if the number of failures in 1,000 entry attempts was the same as the number of failures in 1,000 exit attempts. A random sample of eight delivery trucks was selected for data collection. Do these sample results show that there is a significant difference between entry and exit gate failures? Use a = 0.01. Entry failures Exit failures Truck 1 44 45 Truck 2 43 52 Truck 3 51...
The number of accidents in a month at a certain intersection, denoted by X, has been found to follow the Poisson distribution with its mathematical expectation, that is, E(X), equal to 6. What is the probability that X is larger than 4 in a certain month? What is the probability that X is no more than 1 in a certain month? 1) The probability that X is larger than 4 in a certain month is: Pr(X>4)= 2) The probability that...
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