Question
In: Math
If the moment-generating function of X is M(t) = exp(3 t + 12.5 t2) = e3...
If the moment-generating function of X is M(t) = exp(3 t + 12.5 t2) = e3 t + 12.5 t2.
a. Find the mean and the standard deviation of X.
Mean =
standard deviation =
b. Find P(4 < X < 16). Round your answer to 3 decimal places.
c. Find P(4 < X2 < 16). Round your answer to 3 decimal places.
Solutions
milcah answered 11 months agoRelated Solutions
Find the (probability generating function) p.g.f.’s of the following distributions:[3+3=6] •P(X=x) =(exp(−λ)λ^x)/((1−exp(−λ))x!) , for x= 1,2,3,...,...
Find the (probability generating function) p.g.f.’s of the
following distributions:[3+3=6]
•P(X=x) =(exp(−λ)λ^x)/((1−exp(−λ))x!) , for x= 1,2,3,..., and λ
>0.
•P(X=x) =((pq)^x)(1−q^(N+1))^−1,for x= 0,1,..., N; where 0 <
p < 1, p+q= 1.
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...
If the moment generating function is Mx(t) = 1/(1-10t) for t near 0 whats the pdf,...
If the moment generating function is Mx(t) = 1/(1-10t) for t
near 0
whats the pdf, mean, and variance with steps please want to
understand
(a) Suppose that Y is a random variable with moment generating function H(t). Suppose further that...
(a) Suppose that Y is a random variable with moment generating
function H(t). Suppose further that X is a random variable with
moment generating function M(t) given by M(t) = 1/3 (2e ^(3t) +
1)H(t). Given that the mean of Y is 10 and the variance of Y is 12,
then determine the mean and variance of X (Use H(0) = 1).
(b) Suppose that the Moment generating function for X is M(t) =
e^t/( 3 − 2e^t) . Find...
(a) Suppose that Y is a random variable with moment generating function H(t). Suppose further that...
(a) Suppose that Y is a random variable with moment generating
function H(t). Suppose further that X is a random variable with
moment generating function M(t) given by M(t) = 1 3 (2e 3t +
1)H(t). Given that the mean of Y is 10 and the variance of Y is 12,
then determine the mean and variance of X (Use H(0) = 1).
(b) Suppose that the Moment generating function for X is M(t) =
e t 3 − 2e...
Suppose T1 and T2 are iid Exp(1). What is the probability density function of T1+T2? What...
Suppose T1 and T2 are iid Exp(1).
What is the probability density function of
T1+T2?
What is the probability that T1+T2 ≥
3?
Give the density of an exponential distribution, then derive the moment generating function.
Give the density of an exponential distribution, then derive the
moment generating function.
1. Suppose X has a binomial distribution with parameters n and p. Then its moment-generating function...
1. Suppose X has a binomial distribution with parameters n and
p. Then its moment-generating function is M(t) = (1 − p + pe^t ) n
.
(a) Use the m.g.f. to show that E(X) = np and Var(X) = np(1 −
p).
(b) Prove that the formula for the m.g.f. given above is
correct. Hint: the binomial theorem says that Xn x=0 n x a^x
b^(n−x) = (a + b)^n .
2. Suppose X has a Poisson distribution with...
A particular wave pulse is described by the function f(x,t) = (2/??) exp[-(x + ct)²]. Explain...
A particular wave pulse is described by the function f(x,t) =
(2/??) exp[-(x + ct)²]. Explain how to determine the velocity of
the pulse and why that works. In particular, explain why the sign
of c determines the direction of propagation. (In case you aren’t
familiar, “expo” means “exponential” and exp(x) is often used
instead of e? when the argument gets too big to fit comfortably as
an exponent. Not that this question requires knowing any of
this.)
STAT 150 Homework 23. Random Variable X takes integer values and has the Moment Generating Function:...
STAT 150 Homework
23. Random Variable X takes integer values and has the Moment
Generating Function: Mx(t)=
4/(2-e^t) - 6/(3-e^t).
1) What is the variance of X.
2) Find the probability P(X ≤ 2).
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Make-or-Buy Decision Fremont Computer Company has been purchasing carrying cases for its portable computers at a...
- The following costs were incurred for the single product produced during the first year of operations...
- Non-constant growth model: Do=$2.00 required return on equity= 5% g= 9% n=1,2 g=7% n=3,4 g=3% n=5...
- . Find all x ∈ Z143 such that x2Ξ 7 (mod 143). Please explain all steps...
- #Python: A palindrome is a sequence of characters that reads the same backwards as forwards. For...
- Explain an example in which a variable has two different addresses at different places in a...
- Hadley, a thirty-five-year-old physician, has worked at Princeton Plainsboro Hospital for six years. She recently received...
ADVERTISEMENT