8. For each of the following calculate the quantity indicated. [4 points each) (a) Suppose that...
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8. For each of the following calculate the quantity indicated. [4 points each) (a) Suppose that...
Problem 4 (5 points) a. (2 points) Suppose X ~ Gam(2,0.5). Compute the probability P(4 <...
Problem 4 (5 points) a. (2 points) Suppose X ~ Gam(2,0.5). Compute the probability P(4 < X < 6). Explain. b. (3 points) Suppose X ~ Gam(a, 1), where a > 0 and 1 > 0. Determine E[X]. Use this result to compute the expected value of a Gam(2,0.5) random vari- able. Explain (you may want to use the probability density function (PDF) of a Gam(a +1,ß) random variable to compute E[X]).
4. (8 Marks) Suppose X is a random variable best described by a uniformly distribution or...
4. (8 Marks) Suppose X is a random variable best described by a uniformly distribution or probability that ranges from 2 to 11. a) Write down the probability density function f(1). (1.5 points) b) Compute the following: i) mean (1.5 points) ii) standard deviation (1.5 points) iii) P(X < 3.858) (1.5 points) iv) P(-O< X <H+ o) (2 points)
a) In each of the following pmfs, find the value of C. i) p(x) Cx, x...
a) In each of the following pmfs, find the value of C. i) p(x) Cx, x 1, 2, 3, 4, 5 ii) p(x) C/x, 2,4,8, 16 b) Assume that the pmf of a discrete random variable X is given by px (x) = 20x-, x = 1, 2, 3, Calculate the following probabilities: i) P(X <3) ii) E[X]
(e) Suppose that 4 balls are placed sequentially into one of 5 bins, where the bin...
(e) Suppose that 4 balls are placed sequentially into one of 5 bins, where the bin for each ball is selected at random. For i = 1, 2,3,4,5, define the indicator variables 1, if the ith bin is empty; 0, otherwise Xi _ Then the number of empty boxes is given by X = X\+X2+ X3 + X4+X5, and we learned from week #7 lecture notes and midterm II that Xi ~ Bernoulli(p) with p = (1 - 2)4 =...
8. Suppose that the joint density of X and Y is given by e if 0<...
8. Suppose that the joint density of X and Y is given by e if 0< I<, 0<y< 0, otherwise. Find P(X > 1 Y = y).
(8 points) Suppose that the number of flaws on an individual tile has the Poisson distribution...
(8 points) Suppose that the number of flaws on an individual tile has the Poisson distribution with param- eter = 1.5. A tile is called non-conforming if it has 2 or more flaws. Suppose that we purchase 6 tiles. What is the probability that 4 or more of the 6 tiles are non-conforming?
6. (8 points) Suppose that the number of flaws on an individual tile has the Poisson...
6. (8 points) Suppose that the number of flaws on an individual tile has the Poisson distribution with param- eter 1 = 1.5. A tile is called non-conforming if it has 2 or more flaws. Suppose that we purchase 6 tiles. What is the probability that 4 or more of the 6 tiles are non-conforming?
7T Problem [1] <15 points> -ĉ on a surface given by r = 5—10,0=1,2=4 →8. Calculate...
7T Problem [1] <15 points> -ĉ on a surface given by r = 5—10,0=1,2=4 →8. Calculate the total flux Ø passing through this surface. Magnetic flux density is given as B = 92 6+92 r r
H.W. #5 - Q #8: 8. Suppose that n-48 seeds are planted and suppose that each...
H.W. #5 - Q #8:
8. Suppose that n-48 seeds are planted and suppose that each seed has a probability p 75% of germinating. Let X be the number of seeds that germinate and use the Central Limit Theorem to estimate the probability P(35 < X < 40) that between 35 and 40 seeds germinate. Don't forget to use a continuity correction.
a) (2.5 points) Suppose we have the two following two datasets: (i) 1, 3, 4, 5,...
a) (2.5 points) Suppose we have the two following two datasets: (i) 1, 3, 4, 5, 7, 10, 11 (ii) 6, 8, 9, 10, 12, 15, 16 For each dataset, calculate by hand the mean, interquartile range, and the standard deviation. Make sure to show step-by-step calculations. b) (1 point) How is list (ii) related to list (i)? How does this relationship carry over to the average? the standard deviation? ECONOMETRIX COURSE
Problem 4 (5 points) a. (2 points) Suppose X ~ Gam(2,0.5). Compute the probability P(4 < X < 6). Explain. b. (3 points) Suppose X ~ Gam(a, 1), where a > 0 and 1 > 0. Determine E[X]. Use this result to compute the expected value of a Gam(2,0.5) random vari- able. Explain (you may want to use the probability density function (PDF) of a Gam(a +1,ß) random variable to compute E[X]).
4. (8 Marks) Suppose X is a random variable best described by a uniformly distribution or probability that ranges from 2 to 11. a) Write down the probability density function f(1). (1.5 points) b) Compute the following: i) mean (1.5 points) ii) standard deviation (1.5 points) iii) P(X < 3.858) (1.5 points) iv) P(-O< X <H+ o) (2 points)
a) In each of the following pmfs, find the value of C. i) p(x) Cx, x 1, 2, 3, 4, 5 ii) p(x) C/x, 2,4,8, 16 b) Assume that the pmf of a discrete random variable X is given by px (x) = 20x-, x = 1, 2, 3, Calculate the following probabilities: i) P(X <3) ii) E[X]
(e) Suppose that 4 balls are placed sequentially into one of 5 bins, where the bin for each ball is selected at random. For i = 1, 2,3,4,5, define the indicator variables 1, if the ith bin is empty; 0, otherwise Xi _ Then the number of empty boxes is given by X = X\+X2+ X3 + X4+X5, and we learned from week #7 lecture notes and midterm II that Xi ~ Bernoulli(p) with p = (1 - 2)4 =...
8. Suppose that the joint density of X and Y is given by e if 0< I<, 0<y< 0, otherwise. Find P(X > 1 Y = y).
(8 points) Suppose that the number of flaws on an individual tile has the Poisson distribution with param- eter = 1.5. A tile is called non-conforming if it has 2 or more flaws. Suppose that we purchase 6 tiles. What is the probability that 4 or more of the 6 tiles are non-conforming?
6. (8 points) Suppose that the number of flaws on an individual tile has the Poisson distribution with param- eter 1 = 1.5. A tile is called non-conforming if it has 2 or more flaws. Suppose that we purchase 6 tiles. What is the probability that 4 or more of the 6 tiles are non-conforming?
7T Problem [1] <15 points> -ĉ on a surface given by r = 5—10,0=1,2=4 →8. Calculate the total flux Ø passing through this surface. Magnetic flux density is given as B = 92 6+92 r r
H.W. #5 - Q #8:
8. Suppose that n-48 seeds are planted and suppose that each seed has a probability p 75% of germinating. Let X be the number of seeds that germinate and use the Central Limit Theorem to estimate the probability P(35 < X < 40) that between 35 and 40 seeds germinate. Don't forget to use a continuity correction.
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