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Prove the following statements • corr(ax,y) = corr(x,y) • show that if x,y and z are...
Prove the following statements
• corr(ax,y) = corr(x,y)
• show that if x,y and z are independent. Show what happened
to:
cov(x+y,x+z)= ?
• assume x and y are not independent:
cov(ax + b, y)= ?
70 tre la Car
Ex. 36 Show that if Y= aX+ b (a≠0), then Corr(X, Y) = +1 or -1. Under what conditions will p = +1?
Ex. 36Show that if Y= aX+ b (a≠0), then Corr(X, Y) = +1 or -1. Under what conditions will p = +1?
1. Show that Corr(aX + b, cY + d) = Corr(X, Y) using the definition of...
1. Show that Corr(aX + b, cY + d) = Corr(X, Y) using the definition of correlation in page 249, and finding each component first. Correlatiorn DEFINITION The correlation coefficient of X and Y, denoted by Corr(X, Y), or ρχ.r, or just ρ, is defined by Ox-GY
(5) Show Corr(aX + b, cY + d) = Corr(X, Y). Hint: Use results for the covariance and variance.] (5) Show Corr(aX + b, cY + d) = Corr(X, Y). Hint: Use results for the covariance and variance.]
(5) Show Corr(aX + b, cY + d) = Corr(X, Y). Hint: Use results for the covariance and variance.]
(5) Show Corr(aX + b, cY + d) = Corr(X, Y). Hint: Use results for the covariance and variance.]
(5) Show Corr(aX + b, cY + d) = Corr(X, Y). Hint: Use results for the...
(5) Show Corr(aX + b, cY + d) = Corr(X, Y). Hint: Use results for the covariance and variance.]
X and z are independent. Var(x)=1 ; Var(z) = sigma ^2. E(z)= 0 and y= ax+b+z...
X
and z are independent. Var(x)=1 ; Var(z) = sigma ^2. E(z)= 0 and y=
ax+b+z
I) cov(x,y)= ?
ii) corr(x,y)=?
dependent Varvane 2.
= Var(X) and σ, 1. Let X and Y be random variables, with μx = E(X),...
= Var(X) and σ, 1. Let X and Y be random variables, with μx = E(X), μY = E(Y), Var(Y). (1) If a, b, c and d are fixed real numbers, (a) show Cov (aX + b, cY + d) = ac Cov(X, Y). (b) show Corr(aX + b, cY +d) pxy for a > 0 and c> O
Let X and Y b Var(Y) (1) If a, b,c and d are fixed real numbers,...
Let X and Y b Var(Y) (1) If a, b,c and d are fixed real numbers, = E(X), μγ E (Y),咳= Var(X) and e ranclom variables. with y a) show Cov(aX +b, cY +d)- ac Cov(X,Y) (b) show Corr(aX + b, cY + d)-PXY for a > 0 and c > 0.
Exercise 1 (1). X, Y are random variables (r.v.) and a,b,c,d are values. Complete the formulas...
Exercise 1 (1). 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) (a) E(aX c) (b) Var(aX + c (d) Var(aX bY c) (e) The covariance between aX +c and 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)
Show that tax then Connor-1 we know coulx, n-coulx, could 1)..)-( 1 June The Conroy Cox,...
Show that tax then Connor-1 we know coulx, n-coulx, could 1)..)-( 1 June The Conroy Cox, which is when Bed and when we Under what condition will.19 lal The value when
Prove the following statements
• corr(ax,y) = corr(x,y)
• show that if x,y and z are independent. Show what happened
to:
cov(x+y,x+z)= ?
• assume x and y are not independent:
cov(ax + b, y)= ?
70 tre la Car
1. Show that Corr(aX + b, cY + d) = Corr(X, Y) using the definition of correlation in page 249, and finding each component first. Correlatiorn DEFINITION The correlation coefficient of X and Y, denoted by Corr(X, Y), or ρχ.r, or just ρ, is defined by Ox-GY
(5) Show Corr(aX + b, cY + d) = Corr(X, Y). Hint: Use results for the covariance and variance.]
(5) Show Corr(aX + b, cY + d) = Corr(X, Y). Hint: Use results for the covariance and variance.]
(5) Show Corr(aX + b, cY + d) = Corr(X, Y). Hint: Use results for the covariance and variance.]
X
and z are independent. Var(x)=1 ; Var(z) = sigma ^2. E(z)= 0 and y=
ax+b+z
I) cov(x,y)= ?
ii) corr(x,y)=?
dependent Varvane 2.
= Var(X) and σ, 1. Let X and Y be random variables, with μx = E(X), μY = E(Y), Var(Y). (1) If a, b, c and d are fixed real numbers, (a) show Cov (aX + b, cY + d) = ac Cov(X, Y). (b) show Corr(aX + b, cY +d) pxy for a > 0 and c> O
Let X and Y b Var(Y) (1) If a, b,c and d are fixed real numbers, = E(X), μγ E (Y),咳= Var(X) and e ranclom variables. with y a) show Cov(aX +b, cY +d)- ac Cov(X,Y) (b) show Corr(aX + b, cY + d)-PXY for a > 0 and c > 0.
Exercise 1 (1). 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) (a) E(aX c) (b) Var(aX + c (d) Var(aX bY c) (e) The covariance between aX +c and 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)
Show that tax then Connor-1 we know coulx, n-coulx, could 1)..)-( 1 June The Conroy Cox, which is when Bed and when we Under what condition will.19 lal The value when
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