3. Suppose that discrete random variables $ X $ and $ Y $ have the following incomplete joint distribution table. \[\begin{array}{c|cc|c}X \backslash Y & 0 & 1 & p_X(x) \\\hline-1 & 0.18 & & \\1 & & 0.6 & \\\hlinep_Y(y) & 0.3 & & \\\end{array}\](a) Complete the table above. Are $ X $ and $ Y $ independent? Briefly explain how you determined this.(b) Find $ E(X + Y) $.(c) Find $ \text{Var}(X + Y) $.

Farmula used V(X+Y)=V(X)+V(Y)-2Cov(X,Y)

Answered: 3. Suppose that discrete random…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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K:56) Somehow you manage to build a fair 3-sided die, equally likely to show 1, 2, or 3 every time it is rolled. You roll the die twice, with the results each time being independent. If X is the maximum of the 2 numbers rolled and Y is the sum of the 2 numbers rolled, find the correlation ρ(X, Y ).
Maximize = 3x +2x, +x, 2.x, +x, +x, s150 Subject to 2x, +2x, +8x, s 200 2x, +3x, +x, 5320 with x 20,x, 20,x, 20 4 B Beta -3 -2 -1 x3 1 3 4 5 6 Beta 1 2 3 4 5 6 B Beta 0,5 1 2 3 -3 8 1,5 -0,5 -14 250 50 -2 75 85 100 160 225 150 70 -1 200 320 170 70 x1 x2 x3 x4 x5 x6 Find the initial solution using the Method of the Minimal Element.
An individual has a vNM utility function over money of u(x) = Vx, where x is final wealth. Assume the individual currently has $16. He is offered a lottery with three possible outcomes; he could gain an extra $9, lose $7, or not lose or gain anything. There is a 15% probability that he will win the extra $9. What probability, p, of losing $7 would make the individual indifferent between to play and to not play the lottery? (Make sure to answer in the form, 0.X, i.e. 0.25) Enter your answer here
Example 2.19 Let X be a random variable with possible values {x1, x2,...x) such that P(X = x) =!v i. Find E(X).
A pseudo-random signal (S) of -3 or 3 is transmitted over a noisy channel. S=-3 is transmitted with probability of 1/3. The received signal, Y, is the sum of the sent signal and the noise, N. The noise is modeled as a normal Gaussian with E[N]=0,var(N)=4 . The received signal is decoded as -3 for Y≤−0.5 and 3 for Y>−0.5. a. What is the probability of error in this system? b. To improve the system, each signal is transmitted three times and output is determine by majority rule (2 or more). What is the new probability of error?
The moment-generating function of the discrete random variable X is 1 M(t) =e 1 1 +. -2t 2t -3t e+ 6. . 3 What is the value of P(X> 1) ) 6.
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Let X; be random variables and M; (t) be their respective moment generating functions, for i = 1, 2, 3. Solve: Suppose that M₁ (t) = 1 +t+t² + t³+... Is this enough information to determine the type of random variable that X₁ is? Explain why or why not. Determine the type of random variable if there is enough information. Determine if it is possible for M₂ (t) = (-1)" -0 (2n)! possible, determine the type of random variable that X₂. -+2n. Explain why or why not. If it is Suppose that that the expectation of X3 is -1 and its second moment is 1. Determine if this is enough information to find the moment generating function of X3 explicitly. Explain why or why not. If it is enough information, compute it explicitly.
18a
Can you please do this problem step by step and can you label which one is mean, variance and pmf of X

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3. Suppose that discrete random variables X and Y have the following incomplete joint distri- bution table. X (b) Find E(X+Y). (c) Find Var(X+Y). Y -1 1 Py (y) 0 1 px (x) 0.18 0.6 0.3 (a) Complete the table above. Are X and Y independent? Briefly explain how you deter- mined this.