Determine the value of sup1≤X≤2 log (E [X]) - E [log (X)], that is, of all random variables X taking values between 1 and 2, find the largest value of log (E [X]) - E [log (X)]. Also interpret what th...
Determine the value of sup1≤X≤2 log (E [X]) - E [log (X)], that is, of all random variables X taking values between 1 and 2, find the largest value of log (E [X]) - E [log (X)]. Also interpret what this question is asking.
Homework Answers
The questions wants to check if the linearity of expectance rule
is valid in case of logarithms.
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Determine the value of sup1≤X≤2 log (E [X]) - E [log (X)], that is, of all random variables X taking values between 1 and 2, find the largest value of log (E [X]) - E [log (X)]. Also interpret what th...
Determine the value of sup1≤X≤2 log (E [X]) - E [log (X)], that is, of all...
Determine the value of sup1≤X≤2 log (E [X]) - E [log (X)], that is, of all random variables X taking values between 1 and 2, find the largest value of log (E [X]) - E [log (X)]. Also interpret what this question is asking.
Let ?1,?2,…,??be a collection of independent discrete random variables that all take the value 1 with...
Let ?1,?2,…,??be a collection of independent discrete random variables that all take the value 1 with probability p and take the value 0 with probability (1-p). a) Compute the mean and the variance of ?1 (which is the same for ?2, ?3, etc.) b) Use your answer to (a) to compute the mean and variance of ?̂ = 1/n (?1 + ?2 + ⋯+ ??), which is the proportion of “ones” observed in the n instances of ??. c) Suppose...
th h. 1. Let the random variables(hand the values equiprobably. Let rhx (a) Find the probability density function (P...
th h. 1. Let the random variables(hand the values equiprobably. Let rhx (a) Find the probability density function (PDF) of r? (10pts) x be independent with h N (0, 1) and x taking on 12 dt? (10pts) as a function of Q(x) = (b) Compute P[r21
th h. 1. Let the random variables(hand the values equiprobably. Let rhx (a) Find the probability density function (PDF) of r? (10pts) x be independent with h N (0, 1) and x taking on...
3. Suppose X, Y are discrete random variables taking values in {-1,0,1) and their joint probability...
3. Suppose X, Y are discrete random variables taking values in {-1,0,1) and their joint probability mass function is 0 X=1 where a, b are two positive real numbers. (i) Find the values of a and b such that X and Y are uncorrelated. (ii) Show that X and Y cannot be independent 0
Let X be a discrete random variable taking integer values 1, 2, ..., 10. It is...
Let X be a discrete random variable taking integer values 1, 2, ..., 10. It is also known that: P(X < 4) = 0.57, PCX 2 4) = 0.71. Then P(X = 4) = A: 0.14|B: 0.28 |C: 0.45 OD: 0.64|E: 0.73 OF: 0.95 Submit Answer Tries 0/5
please help me! 3. Suppose X, Y are discrete random variables taking values in-1,0, 1) and...
please help me!
3. Suppose X, Y are discrete random variables taking values in-1,0, 1) and their joint probability mass function is 0 0 X=1 where a, b are two positive real numbers (i) Find the values of a and b such that X and Y are uncorrelated (ii) Show that X and Y cannot be independent. 0
Please select 2 & 3 2. Let X and Y be discrete random variables taking values...
Please select 2 & 3
2. Let X and Y be discrete random variables taking values 0 or 1 only, and let pr(X = i, Y = j)-pij (jz 1,0;j = 1,0). Prove that X and Y are independent if and only if cov[X,Y) 0 3. If X is a random variable with a density function symmetric about zero and having zero mean, prove that cov[X, X2] 0.
Let X and Y be a random variables taking values 1,2, and 3 with joint I/...
Let X and Y be a random variables taking values 1,2, and 3 with joint I/ 01/8 나.rapis. |probabilitiespxY (1, J) given by the matrix shown: 0 1/2 0 1/8 0 1/8 4 pt. Calculate and sketch joint CDF Fxy(i,j). Find px (i) and pr(i) for ii12, 3. Compute P(X2Y). 3 pt
Let X and Y be random variables, each taking values in the set {0,1,2}, with joint...
Let X and Y be random variables, each taking values in the set {0,1,2}, with joint distribution P[X = 0,Y = 0) = 1/3 P[x = 0, = 1] = 0 P[X = 0, Y = 2] = 1/3 P[X = 1, Y =0] = 0 P X = 1, Y = 1] = 1/9 P[X = 1, Y = 2] = 0 P[X = 2, Y =0] = 1/9 P[X = 2, Y = 1] = 1/9 P[X =...
Suppose X is a random variable taking on possible values 1,2,3 with respective probabilities.4, .5, and...
Suppose X is a random variable taking on possible values 1,2,3 with respective probabilities.4, .5, and .1. Y is a random variable independent from X taking on possible values 2,3,4 with respective probabilities .3,.3, and 4. Use R to determine the following. a) Find the probability P(X*Y = 4) b) Find the expected value of X. c) Find the standard deviation of X. d) Find the expected value of Y. e) Find the standard deviation of Y. f) Find the...
th h. 1. Let the random variables(hand the values equiprobably. Let rhx (a) Find the probability density function (PDF) of r? (10pts) x be independent with h N (0, 1) and x taking on 12 dt? (10pts) as a function of Q(x) = (b) Compute P[r21
th h. 1. Let the random variables(hand the values equiprobably. Let rhx (a) Find the probability density function (PDF) of r? (10pts) x be independent with h N (0, 1) and x taking on...
3. Suppose X, Y are discrete random variables taking values in {-1,0,1) and their joint probability mass function is 0 X=1 where a, b are two positive real numbers. (i) Find the values of a and b such that X and Y are uncorrelated. (ii) Show that X and Y cannot be independent 0
Let X be a discrete random variable taking integer values 1, 2, ..., 10. It is also known that: P(X < 4) = 0.57, PCX 2 4) = 0.71. Then P(X = 4) = A: 0.14|B: 0.28 |C: 0.45 OD: 0.64|E: 0.73 OF: 0.95 Submit Answer Tries 0/5
please help me!
3. Suppose X, Y are discrete random variables taking values in-1,0, 1) and their joint probability mass function is 0 0 X=1 where a, b are two positive real numbers (i) Find the values of a and b such that X and Y are uncorrelated (ii) Show that X and Y cannot be independent. 0
Please select 2 & 3
2. Let X and Y be discrete random variables taking values 0 or 1 only, and let pr(X = i, Y = j)-pij (jz 1,0;j = 1,0). Prove that X and Y are independent if and only if cov[X,Y) 0 3. If X is a random variable with a density function symmetric about zero and having zero mean, prove that cov[X, X2] 0.
Let X and Y be a random variables taking values 1,2, and 3 with joint I/ 01/8 나.rapis. |probabilitiespxY (1, J) given by the matrix shown: 0 1/2 0 1/8 0 1/8 4 pt. Calculate and sketch joint CDF Fxy(i,j). Find px (i) and pr(i) for ii12, 3. Compute P(X2Y). 3 pt
Let X and Y be random variables, each taking values in the set {0,1,2}, with joint distribution P[X = 0,Y = 0) = 1/3 P[x = 0, = 1] = 0 P[X = 0, Y = 2] = 1/3 P[X = 1, Y =0] = 0 P X = 1, Y = 1] = 1/9 P[X = 1, Y = 2] = 0 P[X = 2, Y =0] = 1/9 P[X = 2, Y = 1] = 1/9 P[X =...
Suppose X is a random variable taking on possible values 1,2,3 with respective probabilities.4, .5, and .1. Y is a random variable independent from X taking on possible values 2,3,4 with respective probabilities .3,.3, and 4. Use R to determine the following. a) Find the probability P(X*Y = 4) b) Find the expected value of X. c) Find the standard deviation of X. d) Find the expected value of Y. e) Find the standard deviation of Y. f) Find the...
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