Question 3 Suppose that X, Y and Z are statistically independent random variables, each of them with a x²(2) distribution. (a) Find the moment generating function of U = X +3Y+Z. State clearly and justify all steps taken. (b) Calculate the expectation E(U) using the moment generating function. Hint: You may use without proof the fact that the moment generating function of a x²(v) random variable W is v/2 27) 01². 1 Mw (t) = (1 - 2t) -

Q: help please answer in text form with proper workings and explanation for each and every part and…

A: Detailed explanation:Step 1: Calculate the Mean of x and…

Q: If X is a discrete random variable, and it’s PMF function is given by f(x). What is the correct way…

A: According to the provided information, X is a discrete random variable, and it’s PMF function is…

Q: (b) Let Z be a discrete random variable with E(Z) = 0. Does it necessarily follow that E(Z³) = 0? If…

A: Given that, Z is discrete random variable. We know that,  E(z)= ∑Zi*p(zi) Where p(zi) is the…

Q: If the moment generating function of a random variable X is: (1/3+(2/3)e t ) 5 find P (X > 3).

A: The given moment generating function of a random variable X is 13+23et5.

Q: Example 2.15. Let X be a random variable with the following pdf: + 1. Find its CDF. 2. Evaluate the…

A:

Q: Question 4. Let X and Y be independent Poisson random variables, each with mean 3. Let T =…

A: As per given by the question,  The mean value is given 3. From Poisson distribution, PX=x=λxe-λx!…

Q: Let X be a Poisson random variable with A - :3 and Y be a Poisson random variable with X = 4. Assume…

A:

Q: Question 7 Assume that the moment generating function of a discrete random variable X is given by:…

A:

Q: Let X denote a random variable that takes on any of the values -1, 0, 1 with respective…

A: P(X = −1) = 0.2,P(X = 0) = 0.5,P(X = 1) = 0.3.

Q: Consider the discrete random variable x with probability distribution p(x). Denote the mean and…

A:

Q: adom variables, each of them with a x'(2) distribution. a) Find the moment generating function of U…

A:

Q: Let x be a Poisson random variable with mean = 6. Find the probabilities for x using the Poisson…

A: The variable x be a Poisson random variable with mean .

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: Let f(x)= cx for 1 3.2).

A: Obtain the value of C. The value of C is obtained as follows; Probability Density function: Thus,…

Q: Question 23. (a) Use the expectation operator to show that for any random variable Y, Var(Y) = E(Y²)…

A: Solution: Part a) Variance is defined as the average of the squared differences from the mean. That…

Q: A noisy resistor presents a voltage X distributed as a Gaussian random variable with zero mean and…

A: X : voltage of a noisy resistor    Therefore,  X ~ N(mean : μ = 0, standard deviation : σ = 2 =…

Q: If a random variable X follows the process below, dX; = -kX;dt + odWt, W is a standard Brownian…

A: A random variable is a numerical description of the outcome of a statistical experiment. A random…

Q: Let X; be independent Uniform(-7,7) random variables, for i=1, 2, ..., 7. Let Y=X₁+X₂+...+X7. (b)…

A:

Q: A Gamma random variable with expected value n and variance equal 2n, where n is a natural number,…

A: The parameters are estimated as follows: EX=αβ=nVX=αβ2=2nβ=VXEX=2nn=2α=n2

Q: X is a discrete random variable with probability mass function 4 ƒ(x) = cx² for x = Find the value…

A: We have to determine value of c.