Homework Answers
e(x^2) is wrong dude. check again. its 93/2 which is 46.5
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6. Let X be a random variable with the following probability distribution: r -3 6 9...
Let X be a binomial random variable with the probability distribution f(x) shown below. Find the...
Let X be a binomial random variable with the probability distribution f(x) shown below. Find the probability distribution of the random variable Y = x2. 3-X ; x = 0, 1, 2, 3 f(x) = elsewhere Complete the probability distribution g(y) of the random variable Y = x². 3-2/ , y=0,1 g(y) = elsewhere (Type exact answers, using radicals as needed. Use integers or fractions for any numbers in the expressions. Simplify your answers. Use a comma to separate answers...
3. The probability distribution of the discrete random variable X is f(x) = 2 x 1...
3. The probability distribution of the discrete random variable X is f(x) = 2 x 1 8 x 7 8 2−x , x = 0, 1, 2. Find the mean of X. 4. The random variable X, representing the number of errors per 100 lines of software code, has the following probability distribution: x 1 2 3 5 6 f(x) 0.03 0.37 0.2 0.25 0.15 (a) Find E(X). (b) Find E(X2 ). 5. Use the distribution from Problem 4. (a)...
- ACUJU 1. (6%) Let X be a random variable with probability distribution (1+x **,-1<x< 1...
- ACUJU 1. (6%) Let X be a random variable with probability distribution (1+x **,-1<x< 1 0, elsewhere Find the probability distribution of the random variable Y = X2.
Let X be a random variable with probability density function 2 (r > 1 0 otherwise....
Let X be a random variable with probability density function 2 (r > 1 0 otherwise. (a) Compute F)-P(X ) (the cumulative distribution function) for 1. Note that F(x) 0 for 1 (b) Let u-F(z). Invert F(-) to obtain 2 marks [1 mark 3 marks) F-1 (u), (z as a function of Your function should have:- Input: n - Number of samples to be generated. . Output: x - (xi, x2,, n) A vector x of n values from the...
1. (10 marks) random variable with density r(x). Let g: R - (a) Let X R...
1. (10 marks) random variable with density r(x). Let g: R - (a) Let X R be a (differentiable) function and let Y = g(X). Write expressions for the following ((ii)-(iv) should be in terms of the density of X (i) The integral f()d (ii) The mean E(X) (ii The probability P(X e (a, b) (iv) The mean E(g(X)) R be a smooth (1 mark (1 mark) (1 mark (1 mark) (b) Let z E R be a constant and...
Recall that a discrete random variable X has Poisson distribution with parameter λ if the probability...
Recall that a discrete random variable X has Poisson
distribution with parameter λ if the probability mass function of
X
Recall that a discrete random variable X has Poisson distribution with parameter λ if the probability mass function of X is r E 0,1,2,...) This distribution is often used to model the number of events which will occur in a given time span, given that λ such events occur on average a) Prove by direct computation that the mean of...
Let X be a binomial random variable with the probability distribution f(x) shown below. Find the...
Let X be a binomial random variable with the probability distribution f(x) shown below. Find the probability distribution of the random variable Y =X4. 3-x f(x)= H , = 0, 1, 2, 3 f(x) = { elsewhere Complete the probability distribution g(y) of the random variable Y = X*. elsewhere (Type exact answers, using radicals as needed. Use integers or fractions for any numbers in the expressions. Simplify your answers. Use a comma to separate answers as needed.) icals as...
Problem 4 Let X be a discrete random variable with probability mass function fx(x), and let...
Problem 4 Let X be a discrete random variable with probability mass function fx(x), and let t be a function. Define Y = t(X): that is, Y is the randon variable obtained by applying the function t to the value of X Transforming a random variable in this way is frequently done in statistics. In what follows, let R(X) denote the possible values of X and let R(Y) denote the possible values of To compute E[Y], we could irst find...
Let X be a random variable with probability density function fx(2, -1 9. f(y) y> 9. Submit Answe...
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Let X be a random variable with probability density function fx(2, -1 <z<3, 0 otherwise. Find the probability distribution of Y-X2 for 0 < y < 1, 1 < y < 9, and y > 9. [Obviously, fy(y)-0 for y < 0.1 Case 1: O < y < 1. Enter a formula below. Use * for multiplication, / for divison, ^ for power and sqrt for square root. For example, sqrt y...
3. Suppose X,,X2,, is a random sample from a standard normal distribution and let Z be...
3. Suppose X,,X2,, is a random sample from a standard normal distribution and let Z be another standard normal variable that is independent of X,X, X, UX , and V X- 9 9 Let X (x - x)2 i-1 Determine the distribution of each of the variables X, U and V. (a) (b) Determine the distribution of the variable 32 VU Determine the distribution of the variable (c) (d) (e) Determine the distribution of the variable y (where Y is...
Let X be a binomial random variable with the probability distribution f(x) shown below. Find the probability distribution of the random variable Y = x2. 3-X ; x = 0, 1, 2, 3 f(x) = elsewhere Complete the probability distribution g(y) of the random variable Y = x². 3-2/ , y=0,1 g(y) = elsewhere (Type exact answers, using radicals as needed. Use integers or fractions for any numbers in the expressions. Simplify your answers. Use a comma to separate answers...
- ACUJU 1. (6%) Let X be a random variable with probability distribution (1+x **,-1<x< 1 0, elsewhere Find the probability distribution of the random variable Y = X2.
Let X be a random variable with probability density function 2 (r > 1 0 otherwise. (a) Compute F)-P(X ) (the cumulative distribution function) for 1. Note that F(x) 0 for 1 (b) Let u-F(z). Invert F(-) to obtain 2 marks [1 mark 3 marks) F-1 (u), (z as a function of Your function should have:- Input: n - Number of samples to be generated. . Output: x - (xi, x2,, n) A vector x of n values from the...
1. (10 marks) random variable with density r(x). Let g: R - (a) Let X R be a (differentiable) function and let Y = g(X). Write expressions for the following ((ii)-(iv) should be in terms of the density of X (i) The integral f()d (ii) The mean E(X) (ii The probability P(X e (a, b) (iv) The mean E(g(X)) R be a smooth (1 mark (1 mark) (1 mark (1 mark) (b) Let z E R be a constant and...
Recall that a discrete random variable X has Poisson
distribution with parameter λ if the probability mass function of
X
Recall that a discrete random variable X has Poisson distribution with parameter λ if the probability mass function of X is r E 0,1,2,...) This distribution is often used to model the number of events which will occur in a given time span, given that λ such events occur on average a) Prove by direct computation that the mean of...
Let X be a binomial random variable with the probability distribution f(x) shown below. Find the probability distribution of the random variable Y =X4. 3-x f(x)= H , = 0, 1, 2, 3 f(x) = { elsewhere Complete the probability distribution g(y) of the random variable Y = X*. elsewhere (Type exact answers, using radicals as needed. Use integers or fractions for any numbers in the expressions. Simplify your answers. Use a comma to separate answers as needed.) icals as...
Problem 4 Let X be a discrete random variable with probability mass function fx(x), and let t be a function. Define Y = t(X): that is, Y is the randon variable obtained by applying the function t to the value of X Transforming a random variable in this way is frequently done in statistics. In what follows, let R(X) denote the possible values of X and let R(Y) denote the possible values of To compute E[Y], we could irst find...
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Let X be a random variable with probability density function fx(2, -1 <z<3, 0 otherwise. Find the probability distribution of Y-X2 for 0 < y < 1, 1 < y < 9, and y > 9. [Obviously, fy(y)-0 for y < 0.1 Case 1: O < y < 1. Enter a formula below. Use * for multiplication, / for divison, ^ for power and sqrt for square root. For example, sqrt y...
3. Suppose X,,X2,, is a random sample from a standard normal distribution and let Z be another standard normal variable that is independent of X,X, X, UX , and V X- 9 9 Let X (x - x)2 i-1 Determine the distribution of each of the variables X, U and V. (a) (b) Determine the distribution of the variable 32 VU Determine the distribution of the variable (c) (d) (e) Determine the distribution of the variable y (where Y is...
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