edited by
3,730 views
3 votes
3 votes

Let X1, X2 be two independent normal random variables with means μ1, μ2 and standard deviations σ1, σ2 respectively. Consider Y =X1-X2; µ1=µ2=1, σl=1, σ2=2. Then.

(a) Y is normal distributed with mean 0 and variance 1

(b) Y is normally distributed with mean 0 and variance 5

(c) Y has mean 0 and variance 5, but is NOT normally distributed

(d) Y has mean 0 and variance 1, but is NOT normally distributed 
 

edited by

1 Answer

3 votes
3 votes

$var(X_1) = \sigma^2_1 = 1$

$var(X_2) = \sigma^2_2 = 4$

$\mu_1 = \mu_2 =1$

$X_1 \sim $ $N (\mu_1 , \sigma^2_1 )$

$X_2 \sim $ $N (\mu_2 , \sigma^2_2 )$

$Y = X_1 - X_2$

 $E[X_1 - X_2] = E[X_1] - E[X_2] = \mu_1 - \mu_2 = 0$

$Var(X_1 - X_2) = Var(X_1) + Var(X_2) = 1 + 4 = 5$

$Y \sim $ $N (0 , 5 )$

Option B is correct

edited by

Related questions

0 votes
0 votes
0 answers
2
0 votes
0 votes
0 answers
4
GO Classes asked Feb 4
169 views
Consider a dataset with a raw score \(x = 75\), a mean \(\mu = 70\), and a standard deviation \(\sigma = 5\). Calculate the Z-score using the formula \(z = \frac{x - \mu}...