A Gaussian random variable X has mean 2 and variance 4
a) Find P(X < 3).
(b) Find P(1 < X < 3)
(c) Find P({X > 4}|{X > 3})
(d) Let Y = X^2 . Find E[Y].
Answer to the question is as follows:
a, P(X<3) = P(Z< 3-2 / sqrt(4) = P(Z< .5) = .692
b. P(1<X<3) = P( 1-2 / sqrt(4) <Z< 3-2 / sqrt(4)) = P(-.5<Z<.5) = 2*(.692-.5) = .384
c. P(X>4|X>3) = P(Z>1| Z>.5) = (.16 ) /(1-.692) = .52
d. Y = X^2
E(X^2) = Var(X) + E(X)^2
E(X^2) = 4 + (2)^2 = 8
A Gaussian random variable X has mean 2 and variance 4 a) Find P(X < 3)....
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