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) = e^{3 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

Expert Solution

milcah answered 4 months ago

Next > < Previous

Related 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.

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).

Subjects