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?

Expert Solution

please rate me high.

orchestra answered 2 years ago

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?

1. Let X be the uniform distribution on [-1, 1] and let Y be the uniform...

1. Let X be the uniform distribution on [-1, 1] and let Y be the uniform distribution on [-2,2]. a) what are the p.d.f.s of X and Y resp.? b) compute the means of X, Y. Can you use symmetry? c) compute the variance. Which variance is higher?

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).

Let X and Y be two independent samples of a standard uniform distri- bution. Let Z...

Let X and Y be two independent samples of a standard uniform distri- bution. Let Z be the closest integer to X/Y (i.e. the value that we get by rounding X/Y ). Is Z more likely to be even or odd? (hint: draw the sample space over X and Y and identify the regions where Z is even or odd. Work out when Z = 0, when Z = 1, and so forth)

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).

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 ?1, ?2, ?3 be 3 independent random variables with uniform distribution on [0, 1]. Let...

Let ?1, ?2, ?3 be 3 independent random variables with uniform distribution on [0, 1]. Let ?? be the ?-th smallest among {?1, ?2, ?3}. Find the variance of ?2, and the covariance between the median ?2 and the sample mean ? = 1 3 (?1 + ?2 + ?3).

Let ?1 and ?2 be two independent random variables with uniform distribution on [0, 1]. 1....

Let ?1 and ?2 be two independent random variables with uniform distribution on [0, 1]. 1. Write down the joint cumulative distribution function and joint probability density function of ?1 + ?2 and ?1?2

Let ?1 and ?2 be two independent random variables with uniform distribution on [0, 1]. 1....

Let ?1 and ?2 be two independent random variables with uniform distribution on [0, 1]. 1. Write down the joint cumulative distribution function and joint probability density function of ?1 + ?2 and ?1?2. 2. Write down the covariance between ?1 + ?2 and ?1?2. 3. Let ? be the largest magnitude (absolute value) of a root of the equation ?^2 − ?1? + ?2 = 0. Let ? be the random event that says that the equation ?^2 −?1?...

Let ?1 and ?2 be two independent random variables with uniform distribution on [0, 1]. 1....

Let ?1 and ?2 be two independent random variables with uniform distribution on [0, 1]. 1. Write down the joint cumulative distribution function and joint probability density function of ?1 + ?2 and ?1?2. 2. Write down the covariance between ?1 + ?2 and ?1?2. 3. Let ? be the largest magnitude (absolute value) of a root of the equation ? 2 − ?1? + ?2 = 0. Let ? be the random event which says that the equation ?...

Question

Let X and Y be independent and identical uniform distribution on [0, 1]. Let Z=min(X, Y)....

Solutions

Expert Solution

Related Solutions

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

1. Let X be the uniform distribution on [-1, 1] and let Y be the uniform...

X is an independent standard uniform random variable X ∼ Uniform(0, 1) Y is an independent...

Let X and Y be two independent samples of a standard uniform distri- bution. Let Z...

Let X, Y be independent random variables with X ∼ Uniform([1, 5]) and Y ∼ Uniform([2,...

Let X and Y be uniform random variables on [0, 1]. If X and Y are...

Let ?1, ?2, ?3 be 3 independent random variables with uniform distribution on [0, 1]. Let...

Let ?1 and ?2 be two independent random variables with uniform distribution on [0, 1]. 1....

Let ?1 and ?2 be two independent random variables with uniform distribution on [0, 1]. 1....

Let ?1 and ?2 be two independent random variables with uniform distribution on [0, 1]. 1....