X and Y are independent Exponential random variables with mean=4, λ = 1/2. 1) Find the...

X and Y are independent Exponential random variables with mean=4, λ = 1/2.

1) Find the joint CDF of the random variables X, Y and Find the probability that 4X > Y .

2) Find the expected value of X^3 + X*Y .

Expert Solution

orchestra answered 2 years ago

If X and Y are independent exponential random variables, each having parameter λ = 6, find...

If X and Y are independent exponential random variables, each having parameter λ = 6, find the joint density function of U = X + Y and V = e 2X. The required joint density function is of the form fU,V (u, v) = { g(u, v) u > h(v), v > a 0 otherwise (a) Enter the function g(u, v) into the answer box below. (b) Enter the function h(v) into the answer box below. (c) Enter the value...

Let X, Y be independent exponential random variables with mean one. Show that X/(X + Y...

Let X, Y be independent exponential random variables with mean one. Show that X/(X + Y ) is uniformly distributed on [0, 1]. (Please solve it with clear explanations so that I can learn it. I will give thumbs up.)

Let X, Y, and Z independent random variables with variance 4 and mean 1. Find the...

Let X, Y, and Z independent random variables with variance 4 and mean 1. Find the correlation coefficient between (X-2YX+1) and (4X+Y)

Let X and Y be independent Exponential random variables with common mean 1. Their joint pdf...

Let X and Y be independent Exponential random variables with common mean 1. Their joint pdf is f(x,y) = exp (-x-y) for x > 0 and y > 0 , f(x, y ) = 0 otherwise. (See "Independence" on page 349) Let U = min(X, Y) and V = max (X, Y). The joint pdf of U and V is f(u, v) = 2 exp (-u-v) for 0 < u < v < infinity, f(u, v ) = 0 otherwise....

If Y is a random variable with exponential distribution with mean 1/λ, show that E (Y...

If Y is a random variable with exponential distribution with mean 1/λ, show that E (Y ^ k) = k! / (λ^k), k = 1,2, ...

Suppose X and Y are independent random variables and take values 1, 2, 3, and 4...

Suppose X and Y are independent random variables and take values 1, 2, 3, and 4 with probabilities 0.1, 0.2, 0.3, and 0.4. Compute (a) the probability mass function of X + Y (b) E[X + Y ]?

1. Let X and Y be independent random variables with μX= 5, σX= 4, μY= 2,...

1. Let X and Y be independent random variables with μX= 5, σX= 4, μY= 2, and σY= 3. Find the mean and variance of X + Y. Find the mean and variance of X – Y. 2. Porcelain figurines are sold for $10 if flawless, and for $3 if there are minor cosmetic flaws. Of the figurines made by a certain company, 75% are flawless and 25% have minor cosmetic flaws. In a sample of 100 figurines that are...

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 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 X1, X2,..., Xnbe independent and identically distributed exponential random variables with parameter λ . a)...

Let X1, X2,..., Xnbe independent and identically distributed exponential random variables with parameter λ . a) Compute P{max(X1, X2,..., Xn) ≤ x} and find the pdf of Y = max(X1, X2,..., Xn). b) Compute P{min(X1, X2,..., Xn) ≤ x} and find the pdf of Z = min(X1, X2,..., Xn). c) Compute E(Y) and E(Z).

Question