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Let X, Y are random variables (r.v.) and a, b, c, d are values. Complete the formulas using the expectations E(X), E(Y), variances Var(X), Var(Y) and covariance Cov(X, Y) of variables X, Y : (a) E(ax + c) (b) Var(ax + c) (c) E(ax+by+c) (d) Var(ax + by + c) (e) The covariance between aX + cand by + d, that is, Cov(ax + c, bY + d) (f) The correlation between X, Y that is, Corr(X,Y) (g) The correlation between aX + c and by +d, that is, Corr(ax + c, bY + d)

Let X, Y are random variables (r.v.) and a, b, c, d are values. Complete the formulas using the expectations E(X), E(Y), variances Var(X), Var(Y) and covariance Cov(X, Y) of variables X, Y : (a) E(ax + c) (b) Var(ax + c) (c) E(ax+by+c) (d) Var(ax + by + c) (e) The covariance between aX + cand by + d, that is, Cov(ax + c, bY + d) (f) The correlation between X, Y that is, Corr(X,Y) (g) The correlation between aX + c and by +d, that is, Corr(ax + c, bY + d)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let X, Y are random variables (r.v.) and a, b, c, d are values. Complete the formulas using the expectations E(X), E(Y), variances Var(X), Var(Y) and covariance Cov(X, Y) of variables X, Y : (a) E(ax + c) (b) Var(ax + c) (c) E(ax+by+c) (d) Var(ax + by + c) (e) The covariance between aX + cand by + d, that is, Cov(ax + c, bY + d) (f) The correlation between X, Y that is, Corr(X,Y) (g) The correlation between aX + c and by +d, that is, Corr(ax + c, bY + d)
Transcribed Image Text:Let X, Y are random variables (r.v.) and a, b, c, d are values. Complete the formulas using the expectations E(X), E(Y), variances Var(X), Var(Y) and covariance Cov(X, Y) of variables X, Y : (a) E(ax + c) (b) Var(ax + c) (c) E(ax+by+c) (d) Var(ax + by + c) (e) The covariance between aX + cand by + d, that is, Cov(ax + c, bY + d) (f) The correlation between X, Y that is, Corr(X,Y) (g) The correlation between aX + c and by +d, that is, Corr(ax + c, bY + d)
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