Let X∼Geom(0.6). Find E(1.7^X).
(1 point) Let X~Geom(0.5). Find EC
Problem 4. Let X and Y be independent Geom(p) random variables. Let V - min(X, Y) and Find the joint mass function of (V, W) and show that V and W are independent
8.7. Let (xlp)Geom(p). Suppose that the prior distribution of p is U(0, 1). a. Find the posterior pdf of p. b. Find the posterior mode. c. Find the posterior expectation.
8.7. Let (xlp)Geom(p). Suppose that the prior distribution of p is U(0, 1). a. Find the posterior pdf of p. b. Find the posterior mode. c. Find the posterior expectation.
Problem 8. Suppose that XGeom(p) and Y ~ Geom(r) are independent. Find the probability P(X <Y).
A discrete random variable X follows the geometric distribution
with parameter p, written X ∼ Geom(p), if its distribution function
is
A discrete random variable X follows the geometric distribution with parameter p, written X Geom(p), if its distribution function is 1x(z) = p(1-P)"-1, ze(1, 2, 3, ). The Geometric distribution is used to model the number of flips needed before a coin with probability p of showing Heads actually shows Heads. a) Show that fx(x) is indeed a probability...
Q has Beta[a,b] (a=6, b=5) (X|Q=q) i.i.d Geom[q] therefore E[X|Q] = [1-Q / Q] Var[X] = [1-Q / Q^2] 6.1 E[X] = ? 6.2 Var[X] = ?
The random variable X has the probability density function (x)a +br20 otherwise If E(X) 0.6, find (a) P(X <름) (b) Var(x)
1.7 Let X, X be ii.d., each with probability density f,and let Xa) be the smallest of the X's. Show that Xa is consistent for estimating ξ when (i) f(x)-1 for ξ < x < ξ + 1, f(x) 0 elsewhere; (ii) f(x)-2(x-E) for ξ < x < ξ + 1, f(x)-0 elsewhere: (ii) f(x) for<, f()-0 elsewhere; 120 2. Convergence in Probability and in Law (iv) Suppose that f(x)-0 for all x < ξ. Give a simple condition on...
Assume a Poisson distribution. Find the following probabilities. a. Let λ-5.0, find P(X23). b. Let λ:0.6, find P(X 1 ) c. LetA-6.0, find P(XS2) a. When A 5.0, P(X23)- Round to three decimal places as needed.) b. When λ:0.6, P(X 1,- (Round to three decimal places as needed.) C. When λ-60, P(X4- (Round to three decimal places as needed.) 1
Section 1.7: 4. Let f(x) be the exponential generating funcion of a sequence {%). Find the exponential generating functions for the follow- ing sequences in terms of f(x): (a) fan cl (b) foan (c (nani (e) 0, a,a, , (g) ao,0, a2,0, a,0,... (h) a, a2, a,... 8. (a) A sequence a satisfies the recurrence relation a3an+2, ao0 Find the exponential generating function ΣΧ0Lnz"
Section 1.7: 4. Let f(x) be the exponential generating funcion of a sequence {%). Find the...