Suppose that 80% of the population likes cake.
Suppose that 80% of the population likes cake. (d) Let X ~Geo(1/3). Find P(X is odd)...
Let X, Y Geometric(p) be independent, and let Z a. Find the range of 2. b. Find the PMF of Z c. Find EZ. Let X, Y Geometric(p) be independent, and let Z a. Find the range of 2. b. Find the PMF of Z c. Find EZ.
5. A series of independent Bernoulli(p) trials is performed, labeled 1,2,3,...Let X be the location (label) of the first success observed, and Y be the location of the second success observed. (a) Find the joint PMF of X and Y; give your result as a general formula. (It may help to start by considering specific sequences, such as "001001", where X 3 and 6 (b) Write out thefirst of your PMF in table format, covering the range 1 sX 4,13YS...
Please answer from a-d Problem 2. Let X be a random variable with one of the following cumulative distribution function. 1.2 1,2 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 -1.0 -0.5 0.0 0.5 1.0 1.5 2,0 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 X X Pick the correct cumulative distribution function plot and answer questions: Page 2 of 9 Write down the probability mass function and What is the PMF of X? A. Poisson (3...
Let X denote the number of times you have to play a game in order to win once. Assume attempts are independent, and that the chance of winning each time you play is p. (a) Find the probability that X is even (as a function of p). [Hint: You’ll use a geometric series from calculus.] (b) What happens to your answer to (a) as p → 1?
(b) (3 points) Let p(x) = x + x Show that this function is neither odd nor even Then, show that the function defined by h(x) = P(x) - P(-x)] is an odd function 4. (6 points) (a) (2.5 points) Let f(x) = Vä? - 1 and g(x) = (f)(x) and its domain. . Find the product function
Let X and Y be two independent and identically distributed random variables that take only positive integer values. Their PMF is pX(n)=pY(n)=2−n for every n∈N , where N is the set of positive integers. Fix a t∈N . Find the probability P(min{X,Y}≤t) . Your answer should be a function of t . unanswered Find the probability P(X=Y) . unanswered Find the probability P(X>Y) . Hint: Use your answer to the previous part, and symmetry. unanswered Fix a positive integer k...
Problem D: Suppose X1, .,X, are independent random variables. Let Y be their sum, that is Y 1Xi Find/prove the mgf of Y and find E(Y), Var(Y), and P (8 Y 9) if a) X1,.,X4 are Poisson random variables with means 5, 1,4, and 2, respectively. b) [separately from part a)] X,., X4 are Geometric random variables with p 3/4. i=1
Please answer from b-d as priority! Problem 2. Let X be a random variable with one of the following cumulative distribution function. 1.2 1.2 1.0 1.0 0.8 0.8 0.6 0.6 0.4 F 0.4 0.2 0.2 0.0 0.0 -1.0 -0.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 X Pick the correct cumulative distribution function plot and answer questions: Page 2 of 9 (3 pts) Write down the probability mass function and What is the PMF of...
Let the joint pmf of X and Y be p(x, у) схуг, x-1,2,3, y-12. a) Find constant c that makes p(x, y) a valid joint pmf. c) Are X and Y independent? Justify d) Find P(X+Y> 3) and PCIX-YI # 1)
8. (8 points) Let X1, X2, . . . , X, bea random sample from the geometric distribution with pmf f(aip) (1-P)-p,z1,2,3,..., where 0 <ps 1. Find the maximam likel ihood estimator of p and show that the maximum likelthood estimator is unblased. 8. (8 points) Let X1, X2, . . . , X, bea random sample from the geometric distribution with pmf f(aip) (1-P)-p,z1,2,3,..., where 0