Question

Consider the joint probability distribution below. Complete parts (a) through (c). X 1 2 Y 0 0.50 0.00 1 0.00 0.50 a. Compute the marginal probability distributions for X and Y. X 1 2 P(y) Y 0 0.50 0.00 0.50 1 0.00 0.50 0.50 P(x) 0.50 0.50 (Type integers or decimals.) b. Compute the covariance and correlation for X and Y. Cov(X,Y)= 0.25 (Type an integer or a decimal.) Corr(X,Y) = 1.000 (Round to three decimal places as needed.) c. Compute the mean and variance for the linear function W=7X-7Y. $\mu_W$ = (Type an integer or a decimal) 

          Consider the joint probability distribution below. Complete parts (a) through (c).
X
1
2
Y
0
0.50
0.00
1
0.00
0.50
a. Compute the marginal probability distributions for X and Y.
X
1
2
P(y)
Y
0
0.50
0.00
0.50
1
0.00
0.50
0.50
P(x)
0.50
0.50
(Type integers or decimals.)
b. Compute the covariance and correlation for X and Y.
Cov(X,Y)= 0.25 (Type an integer or a decimal.)
Corr(X,Y) = 1.000 (Round to three decimal places as needed.)
c. Compute the mean and variance for the linear function W=7X-7Y.
$\mu_W$ =  (Type an integer or a decimal)
Show more…
Consider the joint probability distribution below. Complete parts (a) through (c). X 1 2 Y 0 0.50 0.00 1 0.00 0.50 a. Compute the marginal probability distributions for X and Y. X 1 2 P(y) Y 0 0.50 0.00 0.50 1 0.00 0.50 0.50 P(x) 0.50 0.50 (Type integers or decimals.) b. Compute the covariance and correlation for X and Y. Cov(X,Y)= 0.25 (Type an integer or a decimal.) Corr(X,Y) = 1.000 (Round to three decimal places as needed.) c. Compute the mean and variance for the linear function W=7X-7Y. = (Type an integer or a decimal)

Added by Tracy M.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Complete parts (athrough c X t0 0.50 0.00 0.00 0.50 a.Compute the marginal probability dis forXandY X 12 P(y) 0 0.50 0.00 0.50 1 0.00 0.50 0.50 P(x) 0.50 0.60 Type integers or decimals. b.Compute the covariance and correlation for X and Y CovX.Y)=0.25Type an integer or a decimal. CorrX,Y=1.000 Round to three decimal places as needed. c.Compute the mean and vaniance for the linear function W7X7Y.
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Transcript

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00:01 So for this problem, to find our marginal probabilities, for instance, probability that y is equal to zero, we would take the sum of the conditional probabilities.
00:09 So probability that y equals zero, given that x equals 1, plus probability that y equals 0, given that x equals 2.
00:21 Or pardon me, let me correct myself here.
00:25 I shouldn't be saying those as conditional probabilities.
00:27 Rather, we would want to take the sum of the joint events, rather.
00:31 So, clear out leftovers from previous problem, there'd be 0 .15 plus 0 .3.
00:38 For a result of 0 .45 is the probability that y equals 0.
00:44 Probability that y equals 1, 0 .2 plus 0 .35 for results of 0 .55.
00:53 And similarly, we'd have that probability that x equals 0 is equal to 0 .15 plus 0 .2 for a result of 0 .35.
01:03 And probability that x equals 2 would be 0 .3, or pardon me, excuse me, that should be x equals 1 and x equals 2, excuse me, probability that x equals 2 is 0 .3 plus 0 .35 for a result of 0 .65.
01:22 And then for part b, to find the covariance of x and y, we can calculate by taking the expected value of x times y, minus the expected value of x times y, minus the expected value of x times the expected value of y.
01:40 So first to find the expected value of x times y, we want to take the sum of the probability that x and y take on each one, each of their possible values, multiplied by the product of those values.
01:58 So to be rigorous here, i'll be including the terms that would go to zero, but we'd have 0 .15 times 0 times 1, plus 0 .3 times 0 times 2, plus 0 .3 .2, plus 0 .4 .5 .5 .5 .5, plus 2 times 1 times 1 plus 0 .35 times 1 times 2...
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