![4. (10 points) A number x is selected at random in the interval [-1, 2]. Let the event A (xco), B-(x-0.51 < 0.5), and C x> 0.75). (a) (5 pts) Find the probabilities of A, B, C, AnB, and Bnc. (b) (5 pts) Find the probabilities of AUB, AuC, and AuBUC.](http://img.homeworklib.com/questions/f7a46b30-7323-11ea-847b-c32f7e1b9c56.png?x-oss-process=image/resize,w_560)
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4. (10 points) A number x is selected at random in the interval [-1, 2]. Let...
(5) 3. A committee is formed consisting of four executives, two women (Susan and Mary) and...
(5) 3. A committee is formed consisting of four executives, two women (Susan and Mary) and two men (Bill and Peter). A chairperson and a secretary are selected randomly by drawing straws. a) List the sample space and the outcomes comprising each of the following events (you can use shorthand notation for names, a table etc.) A fa woman is appointed chairperson), B- (Bill is appointed secretary), C Mary is appointed secretary), AUB, AUBUC, AnB, Bnc, AUB, AnB' ). b)...
(2) Find their intersection and union: Let A={1,3,5,7,9}, B = {2, 4, 6, 8, 10}, C...
(2) Find their intersection and union: Let A={1,3,5,7,9}, B = {2, 4, 6, 8, 10}, C = {1,2,3,4,5}, (2a) (a) AnB =? (2b (b) AnC =? (c) AUB=? (2c). (d) AUC =? (20) (4) Express the following compound inequality: * <4 AND 3-1 (a) in set-builder notation:) (4a) (b) (graph it on the number line:) - -3 3 (c) (in interval notation:) (4c) (3) Answer the following questions: (if A and B are two sets) (a) (The keyword AND A...
4. Let X be a continuous random variable defined on the interval [1, 10 with probability...
4. Let X be a continuous random variable defined on the interval [1, 10 with probability density function r2 (a) Find the value of c such that p(x) is a valid probability density function. (b) Find the probability that X is larger than 8 or less than 2 (this should be one number! (c) Find the probability that X is larger than some value a, assuming 1 < a< 10 d) Find the probability that X is more than 3
Let the random variable X be a random number with the uniform density curve in the...
Let the random variable X be a random number with the uniform density curve in the figure below. Area = 0.4 Area = 0.5 Area = 0.2 Height = 1 0.3 0.7 0.5 0.8 P(X<0.5 or X > 0.8) P(0.3<X<0.7) (a) (b) Find the following probabilities. P(X 2 0.35) (a) (b) P(X = 0.35) P(0.35 < X < 1.25) (c) P(0.10 < X < 0.20 or 0.6 < X < 0.9) (d) X is not in the interval 0.5 to...
7. Let X be a random number selected from the interval (-1,3]. Find the density function...
7. Let X be a random number selected from the interval (-1,3]. Find the density function of Y = [X].
3. Let X be a continuous random variable defined on the interval 0, 4] with probability...
3. Let X be a continuous random variable defined on the interval 0, 4] with probability density function p(r) e(1 +4) (a) Find the value of c such that p(x) is a valid probability density function b) Find the probability that X is greater than 3 (c) If X is greater than 1, find the probability X is greater than 2 d) What is the probability that X is less than some number a, assuing 0<a<4?
regulations. 100 samples are summarized below. If a sample is random indicate the number of samples...
regulations. 100 samples are summarized below. If a sample is random indicate the number of samples in each of the selected at following events Conforms to specifications - Let A denote the event that a sample is from the stack , Stack emissions (so) emissions (SO.) Stack emissions (NOx) 25 -Let B denote the sample 1 Effluent confirms to specifcations Let C denote the sample 100 from effluent a) AUGC b) Bnc C) A d) An B e) AUB
(5) 2. Let X be the number of packages being mailed by a randomly selected customer at a certain ...
(5) 2. Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose that the distribution of X is as follows: T 1 2 3 p(x) 3 .2 .5 A a random sample of size n-3 is selected. a) find pmf of Xn and construct a histogram, b) give two smallest values of S2, (S2 is the sample variance) and find their probabilities.
(5) 2. Let X be the number of...
A real number is to be selected at random from the interval [-5, 5]. There is...
A real number is to be selected at random from the interval [-5, 5]. There is a probability of 0.7 that the result will fall in the range [-5, -1], and all numbers from that interval have the same relative likelihood. Each number in the range (-1, 3) has twice the relative likelihood as each number in the range [3, 5]. a. Plot the PDF and CDF of the random variable described by this probability distribution. b. Find the probability...
(5) 3. A committee is formed consisting of four executives, two women (Susan and Mary) and two men (Bill and Peter). A chairperson and a secretary are selected randomly by drawing straws. a) List the sample space and the outcomes comprising each of the following events (you can use shorthand notation for names, a table etc.) A fa woman is appointed chairperson), B- (Bill is appointed secretary), C Mary is appointed secretary), AUB, AUBUC, AnB, Bnc, AUB, AnB' ). b)...
(2) Find their intersection and union: Let A={1,3,5,7,9}, B = {2, 4, 6, 8, 10}, C = {1,2,3,4,5}, (2a) (a) AnB =? (2b (b) AnC =? (c) AUB=? (2c). (d) AUC =? (20) (4) Express the following compound inequality: * <4 AND 3-1 (a) in set-builder notation:) (4a) (b) (graph it on the number line:) - -3 3 (c) (in interval notation:) (4c) (3) Answer the following questions: (if A and B are two sets) (a) (The keyword AND A...
4. Let X be a continuous random variable defined on the interval [1, 10 with probability density function r2 (a) Find the value of c such that p(x) is a valid probability density function. (b) Find the probability that X is larger than 8 or less than 2 (this should be one number! (c) Find the probability that X is larger than some value a, assuming 1 < a< 10 d) Find the probability that X is more than 3
Let the random variable X be a random number with the uniform density curve in the figure below. Area = 0.4 Area = 0.5 Area = 0.2 Height = 1 0.3 0.7 0.5 0.8 P(X<0.5 or X > 0.8) P(0.3<X<0.7) (a) (b) Find the following probabilities. P(X 2 0.35) (a) (b) P(X = 0.35) P(0.35 < X < 1.25) (c) P(0.10 < X < 0.20 or 0.6 < X < 0.9) (d) X is not in the interval 0.5 to...
7. Let X be a random number selected from the interval (-1,3]. Find the density function of Y = [X].
3. Let X be a continuous random variable defined on the interval 0, 4] with probability density function p(r) e(1 +4) (a) Find the value of c such that p(x) is a valid probability density function b) Find the probability that X is greater than 3 (c) If X is greater than 1, find the probability X is greater than 2 d) What is the probability that X is less than some number a, assuing 0<a<4?
regulations. 100 samples are summarized below. If a sample is random indicate the number of samples in each of the selected at following events Conforms to specifications - Let A denote the event that a sample is from the stack , Stack emissions (so) emissions (SO.) Stack emissions (NOx) 25 -Let B denote the sample 1 Effluent confirms to specifcations Let C denote the sample 100 from effluent a) AUGC b) Bnc C) A d) An B e) AUB
(5) 2. Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose that the distribution of X is as follows: T 1 2 3 p(x) 3 .2 .5 A a random sample of size n-3 is selected. a) find pmf of Xn and construct a histogram, b) give two smallest values of S2, (S2 is the sample variance) and find their probabilities.
(5) 2. Let X be the number of...
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