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.

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

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

Moment generating functions

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 T be a Kumaraswamy random variable, and X be a Weibull random variable, the T-X...

Let T be a Kumaraswamy random variable, and X be a Weibull random variable, the T-X family will be called the Kumaraswamy-Weibull distribution. Using W[F(x)]=F(x). Obtain (a) both the cdf and pdf of the Kumaraswamy-Weibull distribution. (b) both the hazard and reverse hazard function Kumaraswamy-Weibull distribution. (c) the quantile function Kumaraswamy-Weibull distribution.

Two random variable X; Y has the following joint moment generating function MX;Y (s; t) =...

Two random variable X; Y has the following joint moment generating function MX;Y (s; t) = 0:5 + 0:1et + 0:1es + 0:1es+t + 0:15e2s + 0:05e2s+t Find the probability of Y = 1 given X < 2 Hint: > Find the PGF > Deduce the joint probability mass function PMF fX,Y(x,y) >Plot the PMF on a 3-D plane x, y and z = fX,Y(x,y) or alternatively use Cartesian (x-y) plane with fX,Y(x,y) plots >Use conditional Probability rues to obtain...

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...

Let random variable X be uniformly distributed in interval [0, T]. a) Find the nth moment...

Let random variable X be uniformly distributed in interval [0, T]. a) Find the nth moment of X about the origin. b) Let Y be independent of X and also uniformly distributed in [0, T]. Calculate the second moment about the origin, and the variance of Z = X + Y

Suppose that random variable X 0 = (X1, X2) is such that E[X 0 ] =...

Suppose that random variable X 0 = (X1, X2) is such that E[X 0 ] = (µ1, µ2) and var[X] = σ11 σ12 σ12 σ22 . (a matrix) (i) Let Y = a + bX1 + cX2. Obtain an expression for the mean and variance of Y . (ii) Let Y = a + BX where a' = (a1, a2) B = b11 b12 0 b22 (a matrix). Obtain an expression for the mean and variance of Y . (ii)...

Consider the initial value problem mx′′+cx′+kx=F(t), x(0)=0, x′(0)=0 modeling the motion of a spring-mass-dashpot system initially at rest...

Consider the initial value problem mx′′+cx′+kx=F(t), x(0)=0, x′(0)=0 modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N). Assume that m=2 kilograms, c=8 kilograms per second, k=80 Newtons per meter, and F(t)=80cos(8t) Newtons. Solve the initial value problem. x(t)= Determine the long-term behavior of the system. Is limt→∞x(t)=0? If it is, enter zero. If not, enter a function that approximates x(t) for very large positive values...

The random variable X can take on the values -5, 0, and 5, and the random...

The random variable X can take on the values -5, 0, and 5, and the random variable Y can take on the values 20, 25, and 30. The joint probability distribution of X and Y is given in the following table: Y 20 25 30 X -5 0.15 0.02 0.06 0 0.08 0.05 0.05 5 0.32 0.10 0.17 a. Describe in words and notation the event that has probability 0.17 in the table. . b. Calculate the marginal distribution of...

For a random variable X with a Cauchy distribution with θ = 0 , so that...

For a random variable X with a Cauchy distribution with θ = 0 , so that f(x) =(1/ π)/( 1 + x^2) for -∞ < x < ∞ (a) Show that the expected value of the random variable X does not exist. (b) Show that the variance of the random variable X does not exist. (c) Show that a Cauchy random variable does not have ﬁnite moments of order greater than or equal to one.

Subjects