# Question: Suppose X and Y are independent and exponentially distributed both

Suppose X and Y are independent and exponentially distributed both with unit- mean. Consider the roots of the quadratic equation Z2 + Xz + Y = 0.

(a) Find the probability that the roots are real.

(b) Find the probability that the roots are complex.

(c) Find the probability that the roots are equal.

(a) Find the probability that the roots are real.

(b) Find the probability that the roots are complex.

(c) Find the probability that the roots are equal.

## Answer to relevant Questions

In this problem, we revisit the light bulb. Recall that there were two types of bulbs, long- life (L) and short- life (S) and we were given a box of unmarked bulbs and needed to identify which type of bulbs are in the box. ...Suppose we flip a coin three times, thereby forming a sequence of heads and tails. Form a random vector by mapping each outcome in the sequence to 0 if a head occurs or to 1 if a tail occurs. (a) How many realizations of ...Let, X1, X2, and X3 be a set of three zero- mean Gaussian random variables with a covariance matrix of the form Find the following expected values: (a) E [X1| X2 = x2, X3 = x3] (b) E [X1X2 | X3 = x3] (c) E [X1 X2 X3] In this problem, we formulate an alternative derivation of Equation ( 6.58) which gives the PDF of the order statistic, Ym , which is the th largest of a sequence of random variables, X1 ,X2, XN. Start by writing Ym (y) dy = ...Let be the random vector described. (a) Find the LMMSE estimator of given observation of {X2= x2, X3= x3}. (b) Find the MSE of the estimator in part (a). (c) Explain why we cannot find the MAP or ML estimators in this ...Post your question