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Question.4 [16 Marks] Let X equal the...
Let X equal the weight of the soap contained in a box. Assume that the distribution of X is N(μ = 6.05, σ2 = 0.0004).
Let X equal the weight of the soap contained in a box. Assume that the distribution of X is N(μ = 6.05, σ2 = 0.0004). (a) Compute the probability P(X < 6.0171) (b) A random sample of nine (9) boxes of soap is selected from the production line. Let Y equal the number of boxes that weigh less than 6.0171. What is the distribution of Y? (c) Find the probability that at most two (2) boxes weigh less than 6.0171. (d) Let X̅ be...
Question 1 [12 + 4 =16 marks] A. Let A and B be two events such...
Question 1 [12 + 4 =16 marks] A. Let A and B be two events such that P( A) 0.6 , P(B) 0.4 and P( A B) 0.10. Calculate P( A B). Calculate P( A | B). iii. Are events A and B independent? Justify your answer. iv. Are events A and B mutually exclusive events? Justify your answer. (2 + 2 + 3 + 3 = 10 marks) B. A box contains 20 DVDs,...
A candy company distributes boxes of chocolates with a mixture of creams, toffees and cordials. Suppose...
A candy company distributes boxes of chocolates with a mixture of creams, toffees and cordials. Suppose that the weight of each box is 1 kilogram, but the individual weights of the creams, toffees and cordials vary from box to box. For a randomly selected box, let X = weight of creams and Y =weights of the toffees and the pdf is described as: f(x,y) = 24xy - for(0<=x<=1),(0<=y<=1),(x+y)<=1) 0 elsewhere a. Find the probability that in a given box, the...
ustion 2: (Discrete Random variable)[2+2-4 marks] A factory produces components of which I % is defective....
ustion 2: (Discrete Random variable)[2+2-4 marks] A factory produces components of which I % is defective. The components are in boxes of 10 A box is selected at random (a) Find the probability that the box contains at least 2 defective components. (b) Find the mean and the standard deviation of the distribution Cy e length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2...
21. Let X have a standard normal distribution. Find P (-1.12 is less than or equal...
21. Let X have a standard normal distribution. Find P (-1.12 is less than or equal to X is less than or equal to 0.46 )
help, please Question 6 [2 marks] Let X1, X2, ..., X, be a random sample from...
help, please
Question 6 [2 marks] Let X1, X2, ..., X, be a random sample from the Poisson distribution with mean e. a. Express the VAR,(Xi) as a function o2 = g(e). b. b. Find the M.L.E. of g(0) and show that it is unbiased.
Please give the text answer do not with hand writing, Thanks Question 2 (4 marks) Part...
Please give the text answer do not with hand writing, Thanks
Question 2 (4 marks) Part a) A sample of n-25 observations is drawn from a normal population with μ-100 and o-20. Find the following. i) P(X<96) ii) P(96-X-105) Part b) The amount of time the university professors devote to their jobs per week is normally distributed with a mean of 52 hours and a standard deviation of 6 hours. i) What is the probability that a professor works for...
1. Let X be a normal random variable with mean 16. If P(X < 20) 0.65,...
1. Let X be a normal random variable with mean 16. If P(X < 20) 0.65, find the standard deviation o. 2. The probability that an electronic component will fail in performance is 0.2 Use the normal approximation to Binomial to find the probability that among 100 such components, (a) at least 23 will fail in performance. X 26) (b) between 18 and 26 (inclusive) will fail in performance. That is find P(18 3. If two random variables X and...
(c) Let N~DU(100), and let X have the value 10, 20, 25, or 50 with probability 1/4 each, independent of N. If N > X, repeatedly subtract X from N until the result is X or smaller. Let Y be the...
(c) Let N~DU(100), and let X have the value 10, 20, 25, or 50 with probability 1/4 each, independent of N. If N > X, repeatedly subtract X from N until the result is X or smaller. Let Y be the number left over after this repeated subtraction. The number Y is almost the same as the remainder left over after dividing N into X equal parts, ercept that Y will equal X, not 0, if N is evenly divisible...
PHYS1047 a) Given a random variable x, with a continuous probability distribution function fx) 4 marks...
PHYS1047 a) Given a random variable x, with a continuous probability distribution function fx) 4 marks b) The life expectancy (in days) of a mechanical system has a probability density write down equations for the cumulative distribution C(x) and the survival distribution Px). State a relationship between them. function f(x)=1/x, for x21, and f(x)=0 for x <1. i Find the probability that the system lasts between 0 and I day.2 marks i) Find the probability that the system lasts between...
ustion 2: (Discrete Random variable)[2+2-4 marks] A factory produces components of which I % is defective. The components are in boxes of 10 A box is selected at random (a) Find the probability that the box contains at least 2 defective components. (b) Find the mean and the standard deviation of the distribution Cy e length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2...
help, please
Question 6 [2 marks] Let X1, X2, ..., X, be a random sample from the Poisson distribution with mean e. a. Express the VAR,(Xi) as a function o2 = g(e). b. b. Find the M.L.E. of g(0) and show that it is unbiased.
Please give the text answer do not with hand writing, Thanks
Question 2 (4 marks) Part a) A sample of n-25 observations is drawn from a normal population with μ-100 and o-20. Find the following. i) P(X<96) ii) P(96-X-105) Part b) The amount of time the university professors devote to their jobs per week is normally distributed with a mean of 52 hours and a standard deviation of 6 hours. i) What is the probability that a professor works for...
1. Let X be a normal random variable with mean 16. If P(X < 20) 0.65, find the standard deviation o. 2. The probability that an electronic component will fail in performance is 0.2 Use the normal approximation to Binomial to find the probability that among 100 such components, (a) at least 23 will fail in performance. X 26) (b) between 18 and 26 (inclusive) will fail in performance. That is find P(18 3. If two random variables X and...
(c) Let N~DU(100), and let X have the value 10, 20, 25, or 50 with probability 1/4 each, independent of N. If N > X, repeatedly subtract X from N until the result is X or smaller. Let Y be the number left over after this repeated subtraction. The number Y is almost the same as the remainder left over after dividing N into X equal parts, ercept that Y will equal X, not 0, if N is evenly divisible...
PHYS1047 a) Given a random variable x, with a continuous probability distribution function fx) 4 marks b) The life expectancy (in days) of a mechanical system has a probability density write down equations for the cumulative distribution C(x) and the survival distribution Px). State a relationship between them. function f(x)=1/x, for x21, and f(x)=0 for x <1. i Find the probability that the system lasts between 0 and I day.2 marks i) Find the probability that the system lasts between...
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