Moment generating functions

1.92<img src="//img.wizedu.com/images/8927fd9528656364451cb5688a30485a604738137f2ab.jpg" alt="" width="2400" height="2054">

Question

In: Statistics and Probability

If the MGF of x is Mx(t)=(0.6e^t+0.4)^8.Find variance?

Moment generating functions

Expert Solution

1.92

Anne Kanage answered 3 years ago

If the MGF of a random variable X is of the form mX(t) = (0:4et +...

If the MGF of a random variable X is of the form mX(t) = (0:4et + 0:6)8 (i) Find E[X]. (ii) Find the MGF of the random variable Y=3X+2.

Let X ∼ Normal(μ = 20, σ2 = 4). (a) Give the mgf MX of X....

Let X ∼ Normal(μ = 20, σ2 = 4). (a) Give the mgf MX of X. (b) Find the 0.10 quantile of X. (c) Find an interval within which X lies with probability 0.60. (d) Find the distribution of Y = 3X −10 by finding the mgf MY of Y

Let X ~ exp(λ) MGF of X = λ/(1-t) a) What is MGF of Y =...

Let X ~ exp(λ) MGF of X = λ/(1-t) a) What is MGF of Y = 3X b) Y has a common distribution, what is the pdf of Y? c) Let X1,X2,....Xk be independent and identically distributed with Xi ~ exp(λ) and S = Σ Xi (with i = 1 below the summation symbol, and k is on top of the summation symbol). What is the MGF of S? d) S has a common distribution. What is the pdf of...

Find the solution of the initial-value problem X′(t) = ( −8 −5 5 2 )X X0...

Find the solution of the initial-value problem X′(t) = ( −8 −5 5 2 )X X0 = ( 0 1)

Evaluate the MGF of the aggregate claim amount at t = 0.01, if the number of...

Evaluate the MGF of the aggregate claim amount at t = 0.01, if the number of claims is binomial with parameters n = 100 and p = 0.01, and individual claims sizes are Gamma distributed with parameters alpha = 10 and theta = 5.

−7, 8, 8, 6, 10 find the variance step by step

Assume that X N(12:6; 5:8). Find the following probabilities (note: 5.8 is a variance, not a...

Assume that X N(12:6; 5:8). Find the following probabilities (note: 5.8 is a variance, not a standard deviation) a) P(X > 13:1) b) P(X < 11:2) c) P(X 12:3) (Hint: The answer is the same as that to P(X < 12:3).) d) P(X < 7:8) e) P(X > 9:6) e) P(X > 9:6)

8. For each of the following, identify the distribution based on the MGF. Be sure to...

8. For each of the following, identify the distribution based on the MGF. Be sure to specify name of distribution and value(s) of parameter(s). (a) MX(t) = (0.3 + 0.7 e t ) 9 , t ∈ (−∞,∞). (b) MX(t) = 0.8 e t + 0.2, t ∈ (−∞,∞). (c) MX(t) = e 9(e t−1), t ∈ (−∞,∞). (d) MX(t) = 0.75e t 1−0.25e t , t < − ln 0.25. (e) MX(t) = 0.4e t 1−0.6e t 20, t...

If X(t), t ≥ 0 is a Brownian motion process with drift parameter μ and variance...

If X(t), t ≥ 0 is a Brownian motion process with drift parameter μ and variance parameter σ2 for which X(0)=0, show that -X(t), t ≥ 0 is a Brownian motion process with drift parameter -μ and variance parameter σ2.

Let X = {1, 2, 3}. Find all topologies T on X such that (X, T...

Let X = {1, 2, 3}. Find all topologies T on X such that (X, T ) is regular.