Exercise 5.6. Suppose that X is a random variable which has geometric distribution with parameter p,...
Exercise 5.6. Suppose that X is a random variable which has geometric distribution with parameter p, for some pe (0,1). Compute E[9(X)], where So if t = 0, g(t) = if t +0. 11/t
pls help Exercise 5.6. Suppose that X is a random variable which has geometric distribution with parameter p, for some pe (0,1). Compute E[9(X)], where So if t = 0, g(t) = if t +0. 11/t
Question 1: 1a) Let the random variable X have a geometric distribution with parameter p , i.e., P(X = x) = pq??, x=1,2,... i) Show that P(X > m)=q" , where m is a positive integer. (5 points) ii) Show that P(X > m+n X > m) = P(X>n), where m and n are positive integers. (5 points) 1b) Suppose the random variable X takes non-negative integer values, i.e., X is a count random variable. Prove that (6 points) E(X)=...
4. (9 pts) Suppose the random variable Y has a geometric distribution with parameter p. Let ?? = √?? 3 3 . Find the probability distribution of V 3 4. (9 pts) Suppose the random variable Y has a geometric distribution with parameter p. Let V 3 Find the probability distribution of.
5. Suppose X is a discrete random variable that has a geometric distribution with p= 1. a. Compute P(X > 6). [5] b. Use Markov's Inequality to estimate P(X> 6). [5] c. Use Chebyshev's Inequality to estimate P(X>6). [5] t> 0 6. Let be the probability density function of the continuous 0 t< 0 random variable X. a. Verify that g(t) is indeed a probability density function. [8] b. Find the median of X, i.e. the number m such that...
Exercise 2.23 If X is a discrete random variable having the Poisson distribution with parameter that the probability that X is even is e cosh A. Exercise 2.24 If X is a discrete random variable having the geometric distribution with parameter p. show that the probability that X is greater than k is (1 -p)k à, show
Let X be the random variable with the geometric distribution with parameter 0 < p < 1. (1) For any integer n ≥ 0, find P(X > n). (2) Show that for any integers m ≥ 0 and n ≥ 0, P(X > n + m|X > m) = P(X > n) (This is called memoryless property since this conditional probability does not depend on m.)
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...
Problem 8 (10 points). Let X be the random variable with the geometric distribution with parameter 0 <p <1. (1) For any integer n > 0, find P(X >n). (2) Show that for any integers m > 0 and n > 0, P(X n + m X > m) = P(X>n) (This is called memoryless property since this conditional probability does not depend on m. Dobs inta T obabilita ndomlu abonn liaht bulb indofootin W
3. Let X be a random variable from a geometric distribution with parameter p (P(X- k p(1-P)"-, } k-1 k-1, 2, ...). Find Emin{X, 100