Let A, B, and C be independent random variables, uniformly distributed over [0,6],[0,11], and [0,2] respectively....

Let A, B, and C be independent random variables, uniformly distributed over [0,6],[0,11], and [0,2] respectively. What is the probability that both roots of the equation Ax^2+Bx+C=0 are real?

Expert Solution

milcah answered 4 months ago

Let A, B, and C be independent random variables, uniformly distributed over [0,4], [0,2], and [0,3]...

Let A, B, and C be independent random variables, uniformly distributed over [0,4], [0,2], and [0,3] respectively. What is the probability that both roots of the equation Ax2+Bx+C=0 are real?

1) Let U1, U2, ... be independent random variables, each uniformly distributed over the interval (0,...

1) Let U1, U2, ... be independent random variables, each uniformly distributed over the interval (0, 1]. These random variables represent successive bigs on an asset that you are trying to sell, and that you must sell by time = t, when the asset becomes worthless. As a strategy, you adopt a secret number \Theta and you will accept the first offer that's greater than \Theta . The offers arrive according to a Poisson process with rate \lambda = 1....

2. Let X1, X2, . . . , Xn be independent, uniformly distributed random variables on...

2. Let X1, X2, . . . , Xn be independent, uniformly distributed random variables on the interval [0, θ]. (a) Find the pdf of X(j) , the j th order statistic. (b) Use the result from (a) to find E(X(j)). (c) Use the result from (b) to find E(X(j)−X(j−1)), the mean difference between two successive order statistics. (d) Suppose that n = 10, and X1, . . . , X10 represents the waiting times that the n = 10...

Let X and Y be independent and uniformly distributed random variables on [0, 1]. Find the...

Let X and Y be independent and uniformly distributed random variables on [0, 1]. Find the cumulative distribution and probability density function of Z = X + Y.

Let X and Y be uniformly distributed independent random variables on [0, 1]. a) Compute the...

Let X and Y be uniformly distributed independent random variables on [0, 1]. a) Compute the expected value E(XY ). b) What is the probability density function fZ(z) of Z = XY ? Hint: First compute the cumulative distribution function FZ(z) = P(Z ≤ z) using a double integral, and then differentiate in z. c) Use your answer to b) to compute E(Z). Compare it with your answer to a).

Let X and Y be independent continuous random variables, with each one uniformly distributed in the...

Let X and Y be independent continuous random variables, with each one uniformly distributed in the interval from 0 to1. Compute the probability of the following event. XY<=1/7

Let U and V be independent continuous random variables uniformly distributed from 0 to 1. Let...

Let U and V be independent continuous random variables uniformly distributed from 0 to 1. Let X = max(U, V). What is Cov(X, U)?

Let X, Y and Z be independent random variables, each uniformly distributed on the interval (0,1)....

Let X, Y and Z be independent random variables, each uniformly distributed on the interval (0,1). (a) Find the cumulative distribution function of X/Y. (b) Find the cumulative distribution function of XY. (c) Find the mean and variance of XY/Z.

Let X1,X2,… be a sequence of independent random variables, uniformly distributed on [0,1]. Define Nn to...

Let X1,X2,… be a sequence of independent random variables, uniformly distributed on [0,1]. Define Nn to be the smallest k such that X1+X2+⋯+Xn exceeds cn=n2+12n−−√, namely, Nn = min{k≥1:X1+X2+⋯+Xk>ck} Does the limit limn→∞P(Nn>n) exist? If yes, enter its numerical value. If not, enter −999. unanswered Submit You have used 1 of 3 attempts Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.

Let Y and Z be independent continuous random variables, both uniformly distributed between 0 and 1....

Let Y and Z be independent continuous random variables, both uniformly distributed between 0 and 1. 1. Find the CDF of |Y − Z|. 2. Find the PDF of |Y − Z|.

Question