Answer:
Given that:
Consider a discrete random variable X, which can only take on non-negative integer values with E[X^k] = 0.8, k=1,2... Use the moment generating function approach to find the pmf of , k=0,1,...
here as mgf
comparing it with mgf of discrete pmf :
below is pmf of X:
P(X=0) =0.2
P(X=1) =0.8
anywhere else P(x) =0
(10 points) Consider a discrete random variable X, which can only take on non-negative integer values,...
A discrete random variable X can take values from 1 to 10. Find the variance of X knowing X > 3. (Find V(X|X>3) )
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
can someone explain this? thanks! 4. (Discrete Uniform Distribution, 10 points) Suppose that X has a discrete uniform distri bution on the integers 0 through 9, i.e., PCX = x) = 1/10, VI = 0,1,...,9. Determine the PMF of the random variable Y = 2X +3. 5. (Function of Random Variable, 20 points) Assume X is a random variable with the fol- lowing PMF, PCX = k) = k = 0.1.2.... (which is also known as the Poisson distribution). a....
Find the probability generating function of a discrete random variable with probability mass function given by pX(k) = qk−1p, k = 1,2,..., where p and q are probabilities such that p + q = 1. We shall see later that this is called the geometric distribution function.
The moment generating function ф(t) of random variable X is defined for all values of t by et*p(x), if X is discrete e f (x)dx, if X is continus (a) Find the moment generating function of a Binomial random variable X with parameters n (the total number of trials) and p (the probability of success). (b) If X and Y are independent Binomial random variables with parameters (n1 p) and (n2, p), respectively, then what is the distribution of X...
3. Use the probability generating function Px)(s) to find (a) E[X(10)] (b) VarX(10)] (c) P(X(5)-2) . ( 4.2 Probability Generating Functions The probability generating function (PGF) is a useful tool for dealing with discrete random variables taking values 0,1, 2, Its particular strength is that it gives us an easy way of characterizing the distribution of X +Y when X and Y are independent In general it is difficult to find the distribution of a sum using the traditional probability...
a random variable Z with non-zero Consider probability on all the positive integers, that is PIZ k Cak,k = 1,2,... ,co, where 0 < a < 1. Note that B* = if |B1. k-0 -8 i) Specify the constant C (this should not be expressed as a summation) so that this is a valid function. Explain. (5 Points) probability mass i Specify a procedure for simulating Z, given only a standard uniform random number gener- ator, i.e. UUniform[0,1]. (10 Points)...
Consider the random variable X which can take on three values a − b, a, and a + b for real numbers a and b with b > 0. Moreover, P{X =a−b}=P{X =a+b} and P{X =a−b}=2P{X =a}. (a) Find the variance of X. (b) Find the cumulative distribution function of X.
Let random variable X take values {1,2, ...,10} with pk+1 = P(X - k+ 1) = pk/2. Consider g(x) = IA the Indicator function that takes value 1 if event A is true, 0 otherwise. A = {X > 6}. Find E[g(X)].
plz explain Let X be a discrete random variable that takes on the Ivalues - 1,0lt and suppose P ( X = -1) =P ( X = 1) = 75 A. Find the moment generating Function Mx (t) of x. B. Use the moment generating function to find a formula for the nth moment E(X") of x.