The multidimensional random variables fl= X1 E X2 Yı Y/2 x1 I2 follows N₁(μ, E) where 7 3 5 3 6 0 5 -2 5 2 0 4 2 4 -2 4 (a) Determine all the independent univariate random variables. (b) What is the probability density function for £₁ + 2x2? (c) Let x := and y := [3₁]. Determine the conditional distribu- tion density function p(y|x) and p(x|y = 1).

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I've done part a and b, but it would be nice to have some confirmation on my answers. I'm not entirely sure on part c.

The multidimensional random variables
μ =
1
I2
2731
X1
X2
Y1
Y2
Σ =
follows N₁(μ, E) where
7 3
3 6
5
2
5
2
0 4
0 5
-2
(a) Determine all the independent univariate random variables.
(b) What is the probability density function for x₁ + 2x₂?
-2
(c) Let x :=
and y :=
tion density function p(y|x) and p(x/y = 1).
[y₁]. Determine the conditional distribu-
Transcribed Image Text:The multidimensional random variables μ = 1 I2 2731 X1 X2 Y1 Y2 Σ = follows N₁(μ, E) where 7 3 3 6 5 2 5 2 0 4 0 5 -2 (a) Determine all the independent univariate random variables. (b) What is the probability density function for x₁ + 2x₂? -2 (c) Let x := and y := tion density function p(y|x) and p(x/y = 1). [y₁]. Determine the conditional distribu-
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