Question

In: Statistics and Probability

Let X and Y be random variable follow uniform U[0, 1]. Let Z = X to...

Let X and Y be random variable follow uniform U[0, 1]. Let Z = X to the power of Y. What is the distribution of Z?

Solutions

Expert Solution


Related Solutions

2. Let X be a uniform random variable over the interval (0, 1). Let Y =...
2. Let X be a uniform random variable over the interval (0, 1). Let Y = X(1-X). a. Derive the pdf for Y . b. Check the pdf you found in (a) is a pdf. c. Use the pdf you found in (a) to find the mean of Y . d. Compute the mean of Y by using the distribution for X. e. Use the pdf of Y to evaluate P(|x-1/2|<1/8). You cannot use the pdf for X. f. Use...
Let X and Y be uniform random variables on [0, 1]. If X and Y are...
Let X and Y be uniform random variables on [0, 1]. If X and Y are independent, find the probability distribution function of X + Y
Let X and Y be independent and identical uniform distribution on [0, 1]. Let Z=min(X, Y)....
Let X and Y be independent and identical uniform distribution on [0, 1]. Let Z=min(X, Y). Find E[Y-Z]. Hint: condition on whether Y=Z or not. What is the probability Y=Z?
X is an independent standard uniform random variable X ∼ Uniform(0, 1) Y is an independent...
X is an independent standard uniform random variable X ∼ Uniform(0, 1) Y is an independent standard uniform random variable Y ∼ Uniform(0, 1) U = min(X, Y ) V = max(X, Y ) Find the correlation coefficient of V and U , ρ(U, V) = Correlation(U, V).
1. Let X and Y be independent U[0, 1] random variables, so that the point (X,...
1. Let X and Y be independent U[0, 1] random variables, so that the point (X, Y) is uniformly distributed in the unit square. Let T = X + Y. (a) Find P( 2Y < X ). (b). Find the CDF F(t) of T (for all real numbers t). HINT: For any number t, F(t) = P ( X <= t) is just the area of a part of the unit square. (c). Find the density f(t). REMARK: For a...
Let X be a uniform random variable with pdf f(x) = λe−λx for x > 0,...
Let X be a uniform random variable with pdf f(x) = λe−λx for x > 0, and cumulative distribution function F(x). (a) Show that F(x) = 1−e −λx for x > 0, and show that this function satisfies the requirements of a cdf (state what these are, and show that they are met). [4 marks] (b) Draw f(x) and F(x) in separate graphs. Define, and identify F(x) in the graph of f(x), and vice versa. [Hint: write the mathematical relationships,...
Let X, Y be independent random variables with X ∼ Uniform([1, 5]) and Y ∼ Uniform([2,...
Let X, Y be independent random variables with X ∼ Uniform([1, 5]) and Y ∼ Uniform([2, 4]). a) FindP(X<Y). b) FindP(X<Y|Y>3) c) FindP(√Y<X<Y).
Random variable X is a continuous uniform (0,4) random variable and Y=X^(1/2). (Note: Y is always...
Random variable X is a continuous uniform (0,4) random variable and Y=X^(1/2). (Note: Y is always the positive root.) What is the P[X>=E[X]] ? What is the E[Y] ? what is the P[Y>=E[Y]]? what is the PFD of fY(y)?
The random variable X~uniform(0,1) and Y~Exp(1), and they are independent, find the distibution of Z=2X+Y. Step...
The random variable X~uniform(0,1) and Y~Exp(1), and they are independent, find the distibution of Z=2X+Y. Step by Step please better to have a graph and be organized before you answer
Let X be a continuous random variable that has a uniform distribution between 0 and 2...
Let X be a continuous random variable that has a uniform distribution between 0 and 2 and let the cumulative distribution function F(x) = 0.5x if x is between 0 and 2 and let F(x) = 0 if x is not between 0 and 2. Compute 1. the probability that X is between 1.4 and 1.8 2. the probability that X is less than 1.2 3. the probability that X is more than 0.8 4. the expected value of X...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT