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.
Let X be a random variable which follows truncated binomial distribution with the following p.m.f. P(X=x)...
Show that if X follows a binomial distribution with n, trials and probability of success p,-p,jz 1,2, Hint: Use the moment generating function of Bernoulli random variable) 1. , n and X, are independent then X, follows a binomial distribution.
Let X, Y be independent random variables where X is binomial(n = 4, p = 1/3) and Y is binomial(n = 3,p = 1/3). Find the moment-generating functions of the three random variables X, Y and X + Y . (You may look up the first two. The third follows from the first two and the behavior of moment-generating functions.) Now use the moment-generating function of X + Y to find the distribution of X + Y .
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,...
Let X be a random variable with the following probability density function: 0 otherwise. Using following relationship ueudu a. Show that fy (y) is a valid probability density function b. Show that the moment generating function My (t) =-for t 2 (2-t) c. Obtain the first and second raw moments. d. Using these raw moments determine the mean and variance Let X be a random variable with the following probability density function: 0 otherwise. Using following relationship ueudu a. Show...
Let X be a random variable with cumulative distribution function(a) Find the probability density function fX(x), (b) Find the moment generating function MX(s) for s < 3, (c) Find the mean and variance of X.
Let X be a binomial random variable with n = 5 and p = 0.30 Use the Binomial Tables to obtain the correct probability distribution Find each probability. 1) P(X = 5) 2) P(X ?= 1)
A) Let X be a discrete random variable that follows a binomial distribution with n = 20 and probability of success p = 0.16. What is P(X≤2)? Round your response to at least 3 decimal places. B)A baseball player has a 60% chance of hitting the ball each time at bat, with succesive times at bat being independent. Calculate the probability that he gets at least 2 hits in 11 times at bat. Answer to 3 decimals please. C) A...
Let x be the binomial random variable with n=10 and p = 9 a. Find P(x = 8) and create a cumulative probability table for the distribution. b. Find P( x is less than or equal to 7) and P(x is greater than 7) c. Find the mean, u, the standard deviation, o, and the variance. d. Does the Empirical rule work on this distribution for data that is within one, two or three standard deviations of the mean? Explain....
Derive the moment generating function of the binomial distribution and calculate the mean and variance. p(x)=(*)*(1+p)** x = 0,1,2,...,
Let X be a random variable that follows a binomial distribution with n= 12, and probability of success p = 0.86. a) What is P(X = 10)? Round your response to at least 3 decimal places. Number b) What is P(X > 10)? Round your response to at least 3 decimal places. Number c) What is P(X < 10)? Round your response to at least 3 decimal places. Number