Suppose a random variable X has a pmf p(x) = [3^(x-1)] / [4^x] , x = 1,...
Suppose a random variable X has a pmf p(x) = [3^(x-1)] / [4^x]
, x = 1, 2, ...
(a) Find the moment generating function of X.
(b) Give a realistic example of an experiment that this random
variable can be defined from its sample space.
(c) Find the mean and variance of X.
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Suppose a random variable X has a pmf p(x) = [3^(x-1)] / [4^x]
, x = 1,...
Question 4. [5 marksi Let Xbe a random variable with probability mass function (pmf) A-p for...
Question 4. [5 marksi Let Xbe a random variable with probability mass function (pmf) A-p for -1, 2,... and zero elsewhere (whereq-1-p, 0 <p< (a) Find the moment generating function (mg ofX. C11 (b) Using the result in (a) or otherwise find the expected value and variance of X. C23 (c) Let X, X,., X, be independent random variables all with the pmf fix) above, and let Find the mgf and the cumulant generating function of Y.
Consider a random variable X with RX = {−1, 0, 1} and PMF P(X = −1)...
Consider a random variable X with RX = {−1, 0, 1} and PMF P(X =
−1) = 1/4 , P(X = 0) = 1/2 , P(X = 1) = 1/4 .
a) Determine the moment-generating function (MGF) MX(t) of
X.
b) Obtain the first two derivatives of the MGF to compute E[X]
and Var(X).
Consider a random variable X with Rx = {-1,0,1} and PMF Determine the moment-generating function (MGF) Mx(t) of X b) Obtain the first two derivatives of...
Consider a discrete random variable X with pmf x)-(1-p1 p. defined for x - 1, 2,...
Consider a discrete random variable X with pmf x)-(1-p1 p. defined for x - 1, 2, 3,..The moment generating function for this kind of random variable is M(t)Pe 1-(1-P)et. (a) What is E(X)? O p(1-P) 1-P (a) What is Var(x)? 1-p p2 p(1-P) O p(1-P) o -p
7. Let X a be random variable with probability density function given by -1 < x < 1 fx(x) otherwise (a) Find the...
7. Let X a be random variable with probability density function given by -1 < x < 1 fx(x) otherwise (a) Find the mean u and variance o2 of X (b) Derive the moment generating function of X and state the values for which it is defined (c) For the value(s) at which the moment generating function found in part (b) is (are) not defined, what should the moment generating function be defined as? Justify your answer (d) Let X1,...
The Bernoulli random variable takes values 0 and 1, and has probability function f(x) = (p^x) [(1 − p)^(1−x)]
The Bernoulli random variable takes values 0 and 1, and has probability function f(x) = px (1 − p)1−x(a) By calculating f(0) and f(1), give a practical example of a Bernoulli experiment, and a Bernoulli random variable. (b) Calculate the mean and variance of the Bernoulli random variable.
The geometric random variable X has moment generating function given by EetX) = p(1 – qe*)-7,...
The geometric random variable X has moment generating function given by EetX) = p(1 – qe*)-7, where q = 1- p and 0 < p < 1. Use this to derive the mean and variance of X.
2. A discrete random variable X has the following pmf: p(x)| 1-8 30/4 θ/4 A random...
2. A discrete random variable X has the following pmf: p(x)| 1-8 30/4 θ/4 A random sample of size n 30 produced the following observations:
Let X be a random variable which follows truncated binomial distribution with the following p.m.f. P(X=x)...
Let X be a random variable which follows truncated binomial distribution with the following p.m.f. P(X=x) =((n|x)(p^x)(1−p)^(n−x))/(1−(1−p)^n), if x= 1,2,3,···,n. •Find the moment generating function (m.g.f.) and the probability generating function(p.g.f.). •From the m.g.f./p.g.f., and/ or otherwise, obtain the mean and variance. Show all the necessary steps for full credit.
Suppose that X is a discrete random variable with pmf, p(x), arn x1 and x2 be...
Suppose that X is a discrete random variable with pmf, p(x), arn x1 and x2 be numerical values in the range of X. dCDEFGT-Let- What should be in the blank space? F(0) Fx1)
6. Suppose the moment generating function of a random variable X is My(t) = (1 –...
6. Suppose the moment generating function of a random variable X is My(t) = (1 – 2+)-3, fort € (-1/2,1/2) Use this to determine the mean and variance of X.
Question 4. [5 marksi Let Xbe a random variable with probability mass function (pmf) A-p for -1, 2,... and zero elsewhere (whereq-1-p, 0 <p< (a) Find the moment generating function (mg ofX. C11 (b) Using the result in (a) or otherwise find the expected value and variance of X. C23 (c) Let X, X,., X, be independent random variables all with the pmf fix) above, and let Find the mgf and the cumulant generating function of Y.
Consider a random variable X with RX = {−1, 0, 1} and PMF P(X =
−1) = 1/4 , P(X = 0) = 1/2 , P(X = 1) = 1/4 .
a) Determine the moment-generating function (MGF) MX(t) of
X.
b) Obtain the first two derivatives of the MGF to compute E[X]
and Var(X).
Consider a random variable X with Rx = {-1,0,1} and PMF Determine the moment-generating function (MGF) Mx(t) of X b) Obtain the first two derivatives of...
Consider a discrete random variable X with pmf x)-(1-p1 p. defined for x - 1, 2, 3,..The moment generating function for this kind of random variable is M(t)Pe 1-(1-P)et. (a) What is E(X)? O p(1-P) 1-P (a) What is Var(x)? 1-p p2 p(1-P) O p(1-P) o -p
7. Let X a be random variable with probability density function given by -1 < x < 1 fx(x) otherwise (a) Find the mean u and variance o2 of X (b) Derive the moment generating function of X and state the values for which it is defined (c) For the value(s) at which the moment generating function found in part (b) is (are) not defined, what should the moment generating function be defined as? Justify your answer (d) Let X1,...
The geometric random variable X has moment generating function given by EetX) = p(1 – qe*)-7, where q = 1- p and 0 < p < 1. Use this to derive the mean and variance of X.
2. A discrete random variable X has the following pmf: p(x)| 1-8 30/4 θ/4 A random sample of size n 30 produced the following observations:
Suppose that X is a discrete random variable with pmf, p(x), arn x1 and x2 be numerical values in the range of X. dCDEFGT-Let- What should be in the blank space? F(0) Fx1)
6. Suppose the moment generating function of a random variable X is My(t) = (1 – 2+)-3, fort € (-1/2,1/2) Use this to determine the mean and variance of X.
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