Two random variables, X and Y have ranges Rx {1, 2} and Ry = {1, 2, 3}. X and Y have joint probability mass function given by the following table: Y 1 2 3 X 1 0.12 0.13 0.32 2 0.27 0.05 0.11 (i) Find the marginal probability mass functions fx and fy. (ii) Check whether X and Y are independent. (iii) Find the range and the probability mass function of the random variable X/Y (iv) Calculate the variance of X/Y

Q: Find the expected value of each probability mass function.

A: Given: x P(x) 0 0.05 1 0.13 2 0.31 3 0.3 4 0.07

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A: Given: Y is a discrete random variable with possible values of 1, 2, and 4. The probability mass…

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A: To determine the correlation coefficient between X and Y, first, we need to calculate the covariance…

Q: Q.2) (a) Show that the following function satisfies the properties of a joint probability mass…

A: The  joint probability mass function of random variables (X,Y) is given as:xy111.521.532.5435

Q: 1 A probability density function of a random variable is given by f(x)=; =- 65 expected value, the…

A: A probability density function of a random variable is given by, f(x)=165 5+ 5x  ; 25≤x≤36…

Q: 1. Use the joint probability below to calculate Var(X|Y=y1) [Make sure to show your equations and…

A: Here the joint probability mass function are given and we calculate the marginal probability mass…

Q: You have two fair coins. The first coin is tossed five times. Let the random variable X be the…

A: Let X be the number of heads when we toss the coin five times. Then X represent a Binomial…

Q: I are independent. Eunction of W given L = 2. a formed A = Lx W Find the range

A: *Answer: Since there are multiple questions, according to Bartleby policy we will answer the first 3…

Q: Q1. Given that (x, y) = (3x+2y)/5k if x = 1,5 and y = -2,3, is a joint probability distribution…

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Q: Given the probability distributions for variables X and Y shown to the right, P(x,y) Y compute the…

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Q: I. Let X be the number of courses that thirty part-time students were taking this term. The…

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Q: Consider the two random variable X and Y. They have the following joint probability mass function: 1…

A: The correlation of X and Y is represented by the coefficient of correlation. For two random…

Q: variables X and Y. Using this information answer the questions below. Y=2 4c 2c X=1 X=2 That is, P(X…

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Q: Question B) If the joint pdf of the continuous random variables X and Y is: fxy(x, y) = XY for 0<x<2…

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Q: I. Let X be the number of courses that thirty part-time students were taking this term. The…

A: Given data is  Number of Courses (x) P(x=x) 1 5/10 2 10/30 3 7/30 4 4/30 5 2/30 6…

Q: The joint distribution of two random variables X, Y is described in the following joint Probability…

A: From the given information, the joint probability mass function for X and Y is,

Q: X is a discrete random variable that takes values (1, 2, 3, 4, 5). P(X=3)=0.6 and P(X=5)=0.25. What…

A: The cumulative mass function for X is given by: FXx=PX≤x for -∞≤x≤∞

Q: 3. Find the probability mass function of the random variable Y which represents the number of red…

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Q: The function f (x) = cx², x = 1, -1, 2, -2, 3,-3 In order for the random variable X to be a…

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Q: Let X be a random variable with probability function f(x) = 36 1 49 x² Calculate the variance of X.…

A: f(x)=

Q: X and Y are two discrete random variables, the following table summarizes their joint probability…

A: For a :  P(Y=1)=P(Y=1∩X=0)+P(Y=1∩X=1)0.216=a+0.096a=0.120 For b :…

Q: Let X and Y be random variables with Var(X)=0.64, Var(Y)=0.81, and Cov(X,Y) = 0.5. Find each of the…

A: Part (a) Coefficient of correlation ρ(X,Y)The coefficient of correlation ρ  is defined…

Q: Be quick please

A: The joint probability distribution of X &amp; Y is given as:     X 0 1 2 Y 1 0.1 0.2 0.1 2…

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A: Solution

Q: function: 3y2 ;-1< y< 1 f(y) = 0; Otherwise Compute the Variance of Y. That is, compute Var(Y).…

A: Given,f(y)=3y22; -1&lt;y&lt;10;  otherwise

Q: Homework-1: Suppose a continuous random variable X has the following probability density e 2, x >0…

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Q: b. A fair die is tossed four times. The variable X is the number of sixes obtained in the four…

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Q: The distribution of random variable X can be described by the following probability mass function:…

A: The probability mass function for the X can be defined as:

Q: 7- Let X be a random variable with probability density function x=1,2,5 f(x)=8 O.w. (a) Find the…

A: Result used  Y=ax+b  E(Y)=aE(X)+b  V(Y)=a2V(X)  Var(X)=E(X2)-(E(X))2

Q: a) On a particular trading day, you are going to buy shares of the stock that is the cheapest. Find…

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Q: If Z is a discrete random variable with possible values of -1, 0, and 1, and the probability mass…

A: The standard deviation of Z is calculated as follows:

Q: 5. Two fair dice are rolled. Let X be the maximum of the results of two dice. (a) Probability Mass…

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Q: The 3 month demand for a spare car part has the following probability mass function: x 0 1 2 p(x)…

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Q: 1. 12 P(X = x) 0.25 0.50 0.05 0.20 3.

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Q: et X be a random variable with the following probability distribution. Valuex of X P(X=x) -30 -20…

A: let X be a random variable with the following probability distribution.

Q: box A and box B both contain the numbers 1 2 3 and 4. Construct the probability mass function and…

A: Given, Box A 1 , 2, 3 , 4 Box B 1 , 2, 3 , 4

Q: Consider the formula: P(x) = x2/21, x = 0, 1, 2, 4. Is P(x) a probability mass function? If so, show…

A: Solution: 9. From the given information,

Q: W= X+ 3Y Find the (c) correlations (d) correlation coefficient of V and W

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Q: 4. Suppose the joint PDF of two random variables X and Y are given below. |3(ry? + x²y), if 0 < x <…

A: