4. If the random variable X has an show that for a > 0, b>0, exponential distrib f(x) = x/4, for x ≥ 0, 1 λ P(X> a+b|x> a) = P(X > b).

Q: Suppose n> 1. Let X₁, X₂, mean and variance o². Let X₁ = (a) Var(4X₁-3X₂) DLX21 Xn be independently…

A: Let  are iid with mean  and variance .Let

Q: 2. Suppose that X is a random variable with E(X) = 6 and Var(X) = 4. Find the following: a) Е(4X +…

A:

Q: 5. If X is an exponential random variable with parameter 2, and c > 0, show cX is exponential with…

A: Using transformation of cumulative distribution

Q: 3. If X and Y are independent uniform (0, 1) random variables, show that 2 for a > 0 (a + 1)(a + 2)…

A: X and Y are independent U(0,1) random variables:Objective: Show that:

Q: 3. Let the random variable X have the pmf f(x) = = a) E(X) b) E(X²) c) E(3X²2X + 4) (x+1)² for x =…

A: The provided information is as follows:The probability mass function of  is .

Q: 7. If X is a random variable with fx Let Y = 3√In X. (a) Fx(x) ) = 1, 1<x<e (b) Fy(y) (c) fy(y)

A:

Q: 4. Let X be a random variable taking positive values and assume that E(X) exists. Which of the…

A: Option (I) is correct as E(X2)&gt;= (E(X))2 when we find Variance.

Q: (1) E(E(X)) = E(X) (2) E(X – E(X)) = 0 (3) Var(X) = E(X²) – [E(X)]² (4) Given constants a and b,…

A: Discrete random variable is defined as a variable which can take only specific values. For example…

Q: 2) Let X₁, X₂, X3, X4 be a random sample of size 4 from a population with the following distribution…

A:

Q: Let X be a random variable. (a) Let YaX be another random variable. What is EY, in terms of μ = EX?…

A: Given : X be the random variable  Y=aX

Q: Let X₁, Xn be a random sample from the beta distribution with a = B = 0 and = = {0: 0= 1,2}. Show…

A:

Q: Let X₁, , Xn be a random sample from a large population following a uniform distribution over [0,…

A:

Q: Suppose that the waiting time X (in seconds) for the pedestrian signal at a particular street…

A: The random variable   represents the waiting time for the pedestrian signal. The PDF of random…

Q: 7. A discrete random variable X taking non-negative integer values has probability gen- erating…

A:

Q: Suppose that a random variable X is an Exponential Random Variable with parameter β = 3. (a) What is…

A: Solution: From the given information, X follows an exponential distribution with parameter β=3.

Q: Suppose the random variable, X, follows an exponential distribution with mean 8 (0 ≤ @<∞). Let X₁,…

A: Random variable X follows exponential distribution with mean Random variable X follows exponential…

Q: 2. If X is a random variable taking values 0,1,2,.... and P(X) = ab*, where a and b are positive…

A: i) First part:ii) second part:

Q: For the random variable X with the pmf f (x) = (x² + 4) , P(X = -1| a < 0) x = -2, –1,0, 1,2. Find…

A: Given Information: f(x) = 130x2+4 x = -2, -1, 0 , 1 , 2

Q: Suppose that X₁, X2, X3 are independent and identically distributed random variables with…

A: Given Cdf  F(x)=1-2-x; x≥0

Q: 4. Two independent random variables X₁ and x₂ are both uniformly distributed between 9 and 11. Find…

A:

Q: 3. Consider two random variables X₁ and X₂ whose joint pdf is given by 11/2 for x₁ > 0, x2 > 0, x1 +…

A: We are given joint PDF of X1 and X2 as,f(x1,x2)=12;for x1&gt;0 and x2&gt;0, x1+x2&lt;0…