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3.4-8. A random variable X can have values --4, -1, 2, 3, and 4, each with...
1. The random variable X is Gaussian with mean 3 and variance 4; that is X...
1. The random variable X is Gaussian with mean 3 and variance 4; that is X ~ N(3,4). $x() = veze sve [5] (a) Find P(-1 < X < 5), the probability that X is between -1 and 5 (inclusive). Write your answer in terms of the 0 () function. [5] (b) Find P(X2 – 3 < 6). Write your answer in terms of the 0 () function. [5] (c) We know from class that the random variable Y =...
2. Let y=-3x+4.For the case that X is Gaussian random variable of normal distribution given as...
2. Let y=-3x+4.For the case that X is Gaussian random variable of normal distribution given as N (0,4), find the probability density function of Y. What is the mean and variance of Y
1) 2) 3) 4) 5) Suppose that X is a uniform random variable on the interval...
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Suppose that X is a uniform random variable on the interval (0, 1) and let Y = 1/X. a. Give the smallest interval in which Y is guaranteed to be. Enter -Inf or Inf for – or o. Interval:( b. Compute the probability density function of Y on this interval. fy(y) = Suppose that X ~ Bin(4, 1/3). Find the probability mass function of Y = (X – 2)2. a. List all possible values that...
2) A random variable X has the density function: fr(x) =[u(x-1)-u(x-3)]. Define event B (Xs 2.5)...
2) A random variable X has the density function: fr(x) =[u(x-1)-u(x-3)]. Define event B (Xs 2.5) (a) Find the cumulative distribution function, Fy (x). (b) Find the conditional distribution Fx (x|B). the mean E[X], and variance of X Fx(xB)= E[X)= Variance (e) Sketch both Fy(x) and Fx (x|B) on the same plot. Show all important values. (d) Let the output of random variable X above be applied to a square-law device according to Y 5X2. Find the mean value of...
2. The Pareto random variable with parameters a > 0 and B >0 has probability density...
2. The Pareto random variable with parameters a > 0 and B >0 has probability density function (a) Verify that fx is a density function. (b) Find P[X> 3a) (c) Find the mean and variance of X. What restriction do you have on 3 in computing the mean and variance (a different restriction for each)? (d) Use the probability transform to simulate 1000 Pareto random variables with α-1 and β-5 and find their sample mean and variance. Compare this to...
2) Two statistically-independent random variables, (X,Y), each have marginal probability density,...
2) Two statistically-independent random variables, (X,Y), each have marginal probability density, N(0,1) (e.g., zero-mean, unit-variance Gaussian). Let V-3X-Y, Z = X-Y Find the covariance matrix of the vector,
2) Two statistically-independent random variables, (X,Y), each have marginal probability density, N(0,1) (e.g., zero-mean, unit-variance Gaussian). Let V-3X-Y, Z = X-Y Find the covariance matrix of the vector,
A value=2 A -2 It is known that for a random variable X, the Expectation of...
A value=2
A -2 It is known that for a random variable X, the Expectation of X equals 5, and that the Variance equals 7. A random variable Y is defined as: Y= AX+2A = (INSERT THE VALUE OF A) 3(a) Find the Expectation of Y 3(b) Find the Variance of Y 3(c) Find E[Y) 3(d) Find the Standard Deviation of Y Question 4 (10%) For the following probability density function. What is the probability P(x>0.? SÅ (1-x) -A<x<A
Suppose a random variable X has a pmf p(x) = [3^(x-1)] / [4^x] , x = 1,...
Suppose a random variable X has a pmf p(x) = [3^(x-1)] / [4^x] , x = 1, 2, ... (a) Find the moment generating function of X. (b) Give a realistic example of an experiment that this random variable can be defined from its sample space. (c) Find the mean and variance of X.
Page 13 of 13 15. (3 points each) Let X be a random variable with a...
Page 13 of 13 15. (3 points each) Let X be a random variable with a mean of 10 and a variance of 4. Let Y be a random variable with a mean of 8 and a variance of 3. The covariance of X and Y is Oy 0.2. Let W-6Y-4X + 2 a. Find E(W) b. Find Var(W)
3. (8 pt, 2 each) (Ross) Let X be a random variable taking values in the...
3. (8 pt, 2 each) (Ross) Let X be a random variable taking values in the finite interval 0, c]. You may assume that X is discrete, though this is not necessary for this problem (a) Show that EX c and EX2 cEX (b) Use the inequalities above to show that Var(X) <c2[u(1-u)] u=EXE[0, 1]. where (e) Use the result of part (b) to show that Var(cx) se/ (d) Use the result in (c) to bound the variance of a...
1. The random variable X is Gaussian with mean 3 and variance 4; that is X ~ N(3,4). $x() = veze sve [5] (a) Find P(-1 < X < 5), the probability that X is between -1 and 5 (inclusive). Write your answer in terms of the 0 () function. [5] (b) Find P(X2 – 3 < 6). Write your answer in terms of the 0 () function. [5] (c) We know from class that the random variable Y =...
2. Let y=-3x+4.For the case that X is Gaussian random variable of normal distribution given as N (0,4), find the probability density function of Y. What is the mean and variance of Y
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Suppose that X is a uniform random variable on the interval (0, 1) and let Y = 1/X. a. Give the smallest interval in which Y is guaranteed to be. Enter -Inf or Inf for – or o. Interval:( b. Compute the probability density function of Y on this interval. fy(y) = Suppose that X ~ Bin(4, 1/3). Find the probability mass function of Y = (X – 2)2. a. List all possible values that...
2) A random variable X has the density function: fr(x) =[u(x-1)-u(x-3)]. Define event B (Xs 2.5) (a) Find the cumulative distribution function, Fy (x). (b) Find the conditional distribution Fx (x|B). the mean E[X], and variance of X Fx(xB)= E[X)= Variance (e) Sketch both Fy(x) and Fx (x|B) on the same plot. Show all important values. (d) Let the output of random variable X above be applied to a square-law device according to Y 5X2. Find the mean value of...
2. The Pareto random variable with parameters a > 0 and B >0 has probability density function (a) Verify that fx is a density function. (b) Find P[X> 3a) (c) Find the mean and variance of X. What restriction do you have on 3 in computing the mean and variance (a different restriction for each)? (d) Use the probability transform to simulate 1000 Pareto random variables with α-1 and β-5 and find their sample mean and variance. Compare this to...
2) Two statistically-independent random variables, (X,Y), each have marginal probability density, N(0,1) (e.g., zero-mean, unit-variance Gaussian). Let V-3X-Y, Z = X-Y Find the covariance matrix of the vector,
2) Two statistically-independent random variables, (X,Y), each have marginal probability density, N(0,1) (e.g., zero-mean, unit-variance Gaussian). Let V-3X-Y, Z = X-Y Find the covariance matrix of the vector,
A value=2
A -2 It is known that for a random variable X, the Expectation of X equals 5, and that the Variance equals 7. A random variable Y is defined as: Y= AX+2A = (INSERT THE VALUE OF A) 3(a) Find the Expectation of Y 3(b) Find the Variance of Y 3(c) Find E[Y) 3(d) Find the Standard Deviation of Y Question 4 (10%) For the following probability density function. What is the probability P(x>0.? SÅ (1-x) -A<x<A
Page 13 of 13 15. (3 points each) Let X be a random variable with a mean of 10 and a variance of 4. Let Y be a random variable with a mean of 8 and a variance of 3. The covariance of X and Y is Oy 0.2. Let W-6Y-4X + 2 a. Find E(W) b. Find Var(W)
3. (8 pt, 2 each) (Ross) Let X be a random variable taking values in the finite interval 0, c]. You may assume that X is discrete, though this is not necessary for this problem (a) Show that EX c and EX2 cEX (b) Use the inequalities above to show that Var(X) <c2[u(1-u)] u=EXE[0, 1]. where (e) Use the result of part (b) to show that Var(cx) se/ (d) Use the result in (c) to bound the variance of a...
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