Question

In: Math

1) The PDF of a Gaussian random variable is given by fx(x). fx(x)= (1/(3*sqrt(2pi) )*e^((x-4)^2)/18 determine...

1) The PDF of a Gaussian random variable is given by fx(x).

fx(x)= (1/(3*sqrt(2pi) )*e^((x-4)^2)/18

determine

a.) P(X > 4) b). P(X > 0). c). P(X < -2).

2) The joint PDF of random variables X and Y is given by

fxy(x,y)=Ke^-(x+y), x>0 , y>0

Determine

a. The constant k.

b. The marginal PDF fX(x).
c. The marginal PDF fY(y).
d. The conditional PDF fX|Y(x|y). Note fX|Y(x|y) = fxy(x,y)/fY(y)

e. Are X and Y independent.

Solutions

Expert Solution

2)

Note that for a function to be a pdf, the cumulative distribution in the given domain should sum up to 1. ( i.e. the volume under the given surface function should be = 1)

The last part can also be done using intuition from part d.

We see that the conditional pdf x|y is same as pdf of x. This means that the occurrence of x doesn't depend on y. Therefore they are independent.

milcah answered 2 hours ago
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