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Mf the random variables X, Y.and Z have the means /X 3.#Y =5,and /7 = 2 the variances 0} 8,0} 12, and 04 18. and covax Y) .covx Z ~3_ and cov(Y. 7 2, lind the covar...

Question

Mf the random variables X, Y.and Z have the means /X 3.#Y =5,and /7 = 2 the variances 0} 8,0} 12, and 04 18. and covax Y) .covx Z ~3_ and cov(Y. 7 2, lind the covariance oU=X+4Y+27 and V=3X-Y-7

Mf the random variables X, Y.and Z have the means /X 3.#Y =5,and /7 = 2 the variances 0} 8,0} 12, and 04 18. and covax Y) .covx Z ~3_ and cov(Y. 7 2, lind the covariance o U=X+4Y+27 and V=3X-Y-7



Answers

Find the expected value for each random variable.
$$\begin{array}{|c|cccc|} \hline {z} & {9} & {12} & {15} & {18} & {21} \\ \hline {P(z)} & {0.14} & {0.22} & {0.38} & {0.19} & {0.07} \\ \hline \end{array}$$

Yeah. This problem we were told that sigma squared for X is fine Insert required for why is three. We would like to find the variance of the random variable dizzy. Doesn't mean you have to acts plus four. Why minus three? The variance of the it was a variance of negative two X plus four Y minus three. Yeah. Which using our themes from the book is the same as two squared times the variance effect Most four square in terms of variants of why. And then that constant on the end does not change the variance. And so we know the variance of that Is five. So this is four times 5 16 times of variants of Y which we know to be three. So this is 20 plus 48 Which is 68. It's our variants of Z is 68.

When this question were given a normally distributed random variable mean 20 ft Standard Deviation 3.7. Well, as for the values of X left and X right that satisfy this condition here and there symmetrically located. So we're going to convert this into Z. So we just say Z Between the left and the right is .65. And that's basically the set of values here as he left, is he right? And from the table were able to get the probability of the less than the left, were able to get this with this times two is equal to one minus 10.6 five, So the probability the less than the left as equals 2.175. Now, our closest value of Z left here, yes -103 So our z right with respect to symmetry is .93. And converting that to X left and X right, using the formula see time's standard deviation plus. The means we get 24.559 And 31.441.


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