Question

In: Statistics and Probability

Consider the two dependent discrete random variables X and Y . The variable X takes values...

Consider the two dependent discrete random variables X and Y . The
variable X takes values in {−1, 1} while Y takes values in {1, 2, 3}. We observe that

P(Y =1|X=−1)=1/6
P(Y =2|X=−1)=1/2
P(Y =1|X=1)=1/2
P(Y =2|X=1)=1/4
P(X = 1) = 2/ 5
(a) Find the marginal probability mass function (pmf) of Y .
(b) Sketch the cumulative distribution function (cdf) of Y .
(c) Compute the expected value E(Y ) of Y .
(d) Compute the conditional expectation E[Y |X = 1].

Solutions

Expert Solution


Related Solutions

Question 1: Two jointly distributed discrete random variables Consider two discrete random variables X, Y ,...
Question 1: Two jointly distributed discrete random variables Consider two discrete random variables X, Y , taking values in {0, 1, 2, 3} each (for a total of 16 possible points). Their joint probability mass function is given by fXY (x, y) = c · x+1 y+1 . Answer the following questions. (a) What is c? (b) What is the probability that X = Y ? (c) Derive the marginal probability mass functions for both X and Y . (d)...
Assuming X and Y are discrete random variables, X takes value from the set A =...
Assuming X and Y are discrete random variables, X takes value from the set A = {x1, x2, x3, …, xm},and Y takes value from set B = {y1, y2, y3, …, yn}, please answer the following questions 1. If H(X,Y) = H(X) + H(Y), what is the relationship between X and Y? 2. If I(X,Y) = 0, what is the relationship between X and Y? 3. If I(X;Y) = H(X) = H(Y), what is the relationship between X and...
Consider the following data for a dependent variable y and two independent variables, x1and x2. x...
Consider the following data for a dependent variable y and two independent variables, x1and x2. x 1 x 2 y 29 13 94 47 10 109 24 17 113 50 16 178 40 6 95 52 20 176 75 7 171 37 13 118 59 14 142 77 17 211 Round your all answers to two decimal places. Enter negative values as negative numbers, if necessary. a. Develop an estimated regression equation relating y to x1. ŷ =  +  x1 Predict y...
In this problem there are two random variables X and Y. The random variable Y counts...
In this problem there are two random variables X and Y. The random variable Y counts how many times we roll the die in the following experiment: First, we flip a fair coin. If it comes Heads we set X= 1 and roll a fair die until we get a six. If it comes Tails, we set X= 0 and roll the die until we get an even number (2, 4 or 6). a). What are the possible values taken...
1. Assume that X and Y are two independent discrete random variables and that X~N(0,1) and...
1. Assume that X and Y are two independent discrete random variables and that X~N(0,1) and Y~N(µ,σ2).                 a. Derive E(X3) and deduce that E[((Y-µ)/σ)3] = 0                 b. Derive P(X > 1.65). With µ = 0.5 and σ2 = 4.0, find z such that P(((Y-µ)/σ) ≤ z) = 0.95. Does z depend on µ and/or σ? Why
Given two random variables x and y State of Nature   Probability   variable x   variable y I...
Given two random variables x and y State of Nature   Probability   variable x   variable y I 0.2 18 0 II 0. 2 5 -3 III 0.2 12 15 IV 0.2 4 12 V 0.2 6 1 (i) Calculate the mean and variance of each of these variables and the covariance between them (ii) Suppose x and y represent the returns from two assets. Calculate the mean and variance for the following part folios. % in x 125 100 75 50...
Consider the following data for a dependent variable y and two independent variables, x2 and x1....
Consider the following data for a dependent variable y and two independent variables, x2 and x1. x1 x2 y 30 12 94 46 10 109 24 17 113 50 17 179 41 5 94 51 19 175 75 8 171 36 12 118 59 13 143 77 17 212 Round your all answers to two decimal places. Enter negative values as negative numbers, if necessary. a. Develop an estimated regression equation relating y to x1 . Predict y if x1=45....
Consider the following data for a dependent variable y and two independent variables, x1 and x2.
You may need to use the appropriate technology to answer this question. Consider the following data for a dependent variable y and two independent variables, x1 and x2. x1 x2 y 30 12 93 47 10 108 25 17 112 51 16 178 40 5 94 51 19 175 74 7 170 36 12 117 59 13 142 76 16 211 The estimated regression equation for these data is ŷ = −18.89 + 2.02x1 + 4.74x2. Here, SST = 15,276.0,...
Consider the following data for a dependent variable y and two independent variables, x1 and x2....
Consider the following data for a dependent variable y and two independent variables, x1 and x2. x1 x2 y 30 12 94 47 10 108 25 17 112 51 16 178 40 5 94 51 19 175 74 7 170 36 12 117 59 13 142 76 16 209 The estimated regression equation for these data is ŷ = −17.02 + 1.99x1 + 4.70x2. Here, SST = 14,902.9, SSR = 13,773.1, sb1 = 0.2470, and sb2 = 0.9480. (1a) Test...
Consider the following data for a dependent variable y and two independent variables, x1 and x2....
Consider the following data for a dependent variable y and two independent variables, x1 and x2. x1 x2 y 30 13 95 46 10 108 25 18 113 50 16 179 40 5 95 51 20 176 74 7 170 36 12 117 59 13 142 77 16 211 Round your all answers to two decimal places. Enter negative values as negative numbers, if necessary. a. Develop an estimated regression equation relating y to x1. ŷ =_________ +___________ x1 Predict...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT