# probability

Let X and Y be independent continuous random variables that are uniformly distributed on (0,1). Let H=(X+2)Y. Find the probability P(lnH≥z) where z is a given number that satisfies ez<2. Your answer should be a function of z.

Hint: Condition on X.

P(lnH≥z1)= ?

Let X be a standard normal random variable, and let FX(x) be its CDF. Consider the random variable Z=FX(X). Find the PDF fZ(z) of Z. Note that fZ(z) takes values in (0,1) .

fZ(z)= ?

Please, can someone share me the correct answers? I've spent a lot of time trying to solve this problem, but I can't.

1. 👍 13
2. 👎 0
3. 👁 1,031
1. if X and Y are uniform random (0,1) and H=(X+2)Y, then the distribution for H looks like the piecewise graph y={0.4: 0<x<2, 1.2-.4x, 2<x<3}, which i estimated using simulation

1. 👍 1
2. 👎 0
2. upon further consideration (using math not simulation), the function for H is
{0<x<2: ln(3)-ln(2), 2<x<3: ln(3)-ln(x)} (piecewise)

the graph of H:
desmos.com/calculator/jf384j0mrt

the probability graph that P(ln(H)>z):
desmos.com/calculator/io40jln2nx

1. 👍 1
2. 👎 0

## Similar Questions

1. ### probability

Problem 2. Continuous Random Variables 2 points possible (graded, results hidden) Let 𝑋 and 𝑌 be independent continuous random variables that are uniformly distributed on (0,1) . Let 𝐻=(𝑋+2)𝑌 . Find the probability

asked by peter on August 5, 2019
2. ### probability

1) Let X and Y be independent continuous random variables that are uniformly distributed on (0,1) . Let H=(X+2)Y . Find the probability P(lnH≥z) where z is a given number that satisfies e^z

asked by anonymous1 on August 5, 2019
3. ### probability

Let 𝑋 and 𝑌 be independent continuous random variables that are uniformly distributed on (0,1) . Let 𝐻=(𝑋+2)𝑌 . Find the probability 𝐏(ln𝐻≥𝑧) where 𝑧 is a given number that satisfies 𝑒^𝑧

asked by yyyyz on July 28, 2019
4. ### probability

For each of the following sequences, determine the value to which it converges in probability. (a) Let X1,X2,… be independent continuous random variables, each uniformly distributed between −1 and 1. Let

asked by juanpro on April 22, 2014
5. ### Probability

For each of the following sequences, determine the value to which it converges in probability. (a) Let X1,X2,… be independent continuous random variables, each uniformly distributed between −1 and 1. Let

asked by A on April 23, 2014
1. ### Probability

Consider three random variables X, Y, and Z, associated with the same experiment. The random variable X is geometric with parameter p∈(0,1). If X is even, then Y and Z are equal to zero. If X is odd, (Y,Z) is uniformly

asked by qwerty on March 10, 2015
2. ### Math Probability

Let X and Y be independent random variables, each uniformly distributed on the interval [0,2]. Find the mean and variance of XY. E[XY]= var[XY]= Find the probability that XY≥1. Enter a numerical answer. P(XY≥1)=

asked by xyz on May 20, 2014
3. ### Maths Probability

Let X and Y be independent random variables, each uniformly distributed on the interval [0,2]. Find the mean and variance of XY. E[XY]= 1 var[XY]= ??? Find the probability that XY≥1. Enter a numerical answer. P(XY≥1)= ???

asked by Anonymous on May 14, 2014
4. ### Probability

Let X,Y,Z be three independent (i.e. mutually independent) random variables, each uniformly distributed on the interval [0,1]. 1. Find the mean and variance of 1/(Z+1). E[1/(Z+1)]= var(1/(Z+1))= 2. Find the mean of XY/(Z+1). Hint:

asked by Anonymous on December 20, 2018
5. ### Probability

Let N,X1,Y1,X2,Y2,… be independent random variables. The random variable N takes positive integer values and has mean a and variance r. The random variables Xi are independent and identically distributed with mean b and variance

asked by qwerty on April 21, 2015

More Similar Questions