Show all steps. Thanks. 2.6.4. A discrete random variable X is such that 2n-1 P(X =...
2.6.5. A discrete random variable X is such that P(X 2") n= 1,2 2" Show that EX-oo. That is, X has no mathematical expectation.
Problem 3. Let X be a discrete random variable that takes values in N. Show that if X is memory-free then it must be the case that X Geo(p) for some p. (Hint a useful first step might be to show that P(X > t)= P(X > 1)' for all t E N.)
Problem 3. Let X be a discrete random variable that takes values in N. Show that if X is memory-free then it must be the case that...
(a) Below is the CDF for a discrete random variable, X if x 1 1/2 if 1 x< 2 if 2 x 3 7/8 if 3 x 4 F(x) = 3/4 2 1 if nx <n+1. Describe the probability 2n In general, note that for any positive integer n, F(x) distribution of X by finding P(X 1), P(X = 2), P(X positive integer n, and describe an experiment that would result in this random variable X. 3), and the general...
A discrete random variable A takes values {1, 2, 4} with probabilities specified as follows: P[A = 1] = 0.5, P[A = 2] = 0.3 and P [A = 4] = 0.2 Given A= ), a discrete random variable N is Poisson distributed with rate equal to 1, that is: 9 P[N = n|A = 1] = in n! el Hint If N is Poisson distributed with rate 1, its expectation and variance are as follows: E[N] = Var [N]...
1 Let X be a discrete random variable. (a) Show that if X has a finite mean μ. then EX-ix-0. (b) Show that if X has a finite variance, then its mean is necessarily finite 2 Let X and Y be random variables with finite mean. Show that, if X and Y are independent, then 3 Let Y have mean μ and finite variance σ2 (a) Use calculus to show that μ is the best predictor of Y under quadratic...
2. For a discrete random variable X, with CDF F(X), it is possible to show that P(a < X S b)-F(b) - F(a), for a 3 b. This is a useful fact for finding the probabil- ity that a random variable falls within a certain range. In particular, let X be a random variable with pmf p( 2 tor c-1,2 a. Find the CDF of X b. Find P(X X 5). c. Find P(X> 4). 3. Let X be a...
3. Consider a discrete random variable X which follows the geometric distribution f(x,p) = pr-1(1-p), x = 1.2. . . . , 0 < p < 1. Recall that E(x) (1-p) (a) Find the Fisher information I(p). (b) Show that the Cramer-Rao inequality is strict e) Let XX ~X. Find the maximum likelihood estimator of p. Note that the expression you find may look complicated and hard to evaluate. (d) Now modify your view by setting μ T1p such that...
Discrete Random Variable. The random variable x has the discrete probability distribution shown here: x -2 -1 0 1 2 p(x) 0.1 0.15 0.4 0.3 0.05 Find P(-1<=x<=1) Find P(x<2) Find the expected value (mean) of this discrete random variable. Find the variance of this discrete random variable
discrete random variable has probability mass function, P(X =
n) = ?1?n.
? 1, forxeven Let Y = −1, for x odd
Find the expected value of Y ; (E[y]).
probability function mass A discrete random variable has P ( X = n) = (3) for x Y = { for Find the expected value of Y CE(y)] Let even x odd
The probability mass function for the discrete random variable X is p(X=0)=0.13; p(X=1)=0.31; p(X=2)=m. What is the expected value of X? Hint: First compute m, then find the expectation of X. Round your answer to the nearest hundredth.