Question

A stick of unit length is broken into two pieces at random: the interval is divided...

A stick of unit length is broken into two pieces at random: the interval is divided in two pieces at X, and X is uniformly distributed in (0,1).

Let Y be the longer piece, therefore range of Y is (1/2,1). Find the cumulative distribution function of Y.

Homework Answers

Answer #1


Please leave a like. Thanks a lot. Feel free to comment below if you need any further assistance, I'll reply ASAP. Have a nice day.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider a stick of length l . We break it randomly into two pieces and keep...
Consider a stick of length l . We break it randomly into two pieces and keep the piece, of length X, that contains the left end of the stick. We then repeat the same process on the piece we keep, and let Y be the length of the remaining piece after breaking the second time. (a) Find the joint p.d.f of X and Y . (b) Find Var(Y |X). (c) Suppose that we break the stick at random point into...
Break a stick of unit length at a uniformly chosen random point. Then take the shorter...
Break a stick of unit length at a uniformly chosen random point. Then take the shorter of the two pieces and break it again in two pieces at a uniformly chosen random point. Let X denote the shortest of the final three pieces. Find the pdf of X.
1) We have a stick of unit length. We break that into 3 pieces using the...
1) We have a stick of unit length. We break that into 3 pieces using the following methods a. We chose randomly and independently two points on the stick using a uniform PDF, and we break stick at these 2 points b. We break the stick at a random point chosen by using a uniform PDF, and then we break the piece that contains the right end of the stick, at a random point chosen by using a uniform PDF...
We are given a stick that extends from 0 to x. Its length, x, is the...
We are given a stick that extends from 0 to x. Its length, x, is the realization of an exponential random variable X, with mean 1. We break that stick at a point Y that is uniformly distributed over the interval [0,x]. Write down the (fully specified) joint PDF fX,Y(x,y) of X and Y. For 0<y≤x: fX,Y(x,y)= Find Var(E[Y∣X]). Var(E[Y∣X])= 3. We do not observe the value of X, but are told that Y=2.2. Find the MAP estimate of X...
The random variable X is uniformly distributed in the interval [0, α] for some α >...
The random variable X is uniformly distributed in the interval [0, α] for some α > 0. Parameter α is fixed but unknown. In order to estimate α, a random sample X1, X2, . . . , Xn of independent and identically distributed random variables with the same distribution as X is collected, and the maximum value Y = max{X1, X2, ..., Xn} is considered as an estimator of α. (a) Derive the cumulative distribution function of Y . (b)...
Included all steps. Thanks The random variable X is uniformly distributed in the interval [0, α]...
Included all steps. Thanks The random variable X is uniformly distributed in the interval [0, α] for some α > 0. Parameter α is fixed but unknown. In order to estimate α, a random sample X1, X2, . . . , Xn of independent and identically distributed random variables with the same distribution as X is collected, and the maximum value Y = max{X1, X2, ..., Xn} is considered as an estimator of α. (a) Derive the cumulative distribution function...
Suppose that X is a random variable uniformly distributed over the interval (0, 2), and Y...
Suppose that X is a random variable uniformly distributed over the interval (0, 2), and Y is a random variable uniformly distributed over the interval (0, 3). Find the probability density function for X + Y .
Choose two numbers X and Y independently at random from the unit interval [0,1] with the...
Choose two numbers X and Y independently at random from the unit interval [0,1] with the uniform density. The probability that X^2+Y^2>0.49 THE ANSWER IS NOT .0192129
Let X1, X2, X3 be independent random variables, uniformly distributed on [0,1]. Let Y be the...
Let X1, X2, X3 be independent random variables, uniformly distributed on [0,1]. Let Y be the median of X1, X2, X3 (that is the middle of the three values). Find the conditional CDF of X1, given the event Y = 1/2. Under this conditional distribution, is X1 continuous? Discrete?
Gloria and Steven are supposed to meet at 2 pm. The number of hours Gloria is...
Gloria and Steven are supposed to meet at 2 pm. The number of hours Gloria is late is distributed uniformly over (0,1). The number of hours Steven is late is distributed according to an exponential random variable with parameter 2. Their respective delays are supposed to be independent. Let X be the time at which Gloria and Steven actually meet (in number of hours after 2 pm). A) Find the cumulative distribution function of X. B) Use it to calculate...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT