a expected number of poops the hamster took in a day= E(X+Y)=E(X)+E(Y) =2+3 =5
b) probability the hamster pooped fewer than 2 times a day=P(X<2) =P(X=0)+P(X=1)
=e-5*500!+e-5*511! =0.0404
Suppose your hamster poops X times before noon and Y times after noon. Where X is...
Problem 4 Bob and Alice plan to meet between noon and 1 pm for lunch at the cafeteria Bob's arrival time, denoted by X, measured in minutes after 12 noon, is a uniform random variable betrwen 0 and Go minutes. The same for Alice's amial time, denoted by Y Bob's and Alice's arrival times are independent. We are interested in the waiting time i. What is the probability that W 10 if X 15? ii. What is the probability that...
QUESTION 4 Suppose Xis a random variable with probability density function f(x) and Y is a random variable with density function f,(x). Then X and Y are called independent random variables if their joint density function is the product of their individual density functions: x, y We modelled waiting times by using exponential density functions if t <0 where μ is the average waiting time. In the next example we consider a situation with two independent waiting times. The joint...
On average, a particular web page is accessed 10 times an hour. Let X be the number of times this web page will be accessed in the next hour. (a) What is E[X] and Var[X]? (b) What is the probability there is at least one access in the next hour? (c) What is the probability there are between 8 and 12 (inclusive) accesses in the next hour? and, Let X be a random variable with image Im(X) = (0, 1,...
Consider the discrete random variables X and Y with the following joint probability mass function: 2 y fxy(x,y) -1 0 1/8 0 -1 1/4 0 1/4 0 1/8 -1 1/8 1 -1 1/8 What is P(X = 1 Y = 0)? Are X and Y independent? 1 1 1 A. 0; independent B. 1/2; independent C. 1/2; dependent D. 1/8; dependent E. none of the preceding 3. Multiple Choice Question Suppose that the number of bad cheques received by a...
Let Y be the number of calls to a particular hotline within 10 min. Suppose Y is a Poisson random... Let Y be the number of calls to a particular hotline within 10 min. Suppose Y is a Poisson random variable with mean of 3. Find the probability that there are at most 4 calls given that there are already 2 calls within the 10 min. THIS IS NOT A STRAIGHTFORWARD CONDITIONAL PROBABILITY! I'VE POSTED THIS TWICE ALREADY AND BOTH...
2. SUPPLEMENTAL QUESTION 1 (a) Toss a fair coin so that with probability pheads occurs and with probability p tails occurs. Let X be the number of heads and Y be the number of tails. Prove X and Y are dependent (b) Now, toss the same coin n times, where n is a random integer with Poisson distribution: n~Poisson(A) Let X be the random variable counting the number of heads, Y the random variable counting the number of tails. Prove...
Q4. (20pts, Binomial and Poisson approximation Suppose a gambler bets (1) ten times on events of probability 1/20, (2) then twenty times on events of probability 1/20, (3) then thirty times on events of probability 1/30, (4) then forty times on events of probability 1/40. Assuming the events are independent. (i) What is the exact distribution of the number of times the gambler wins in (4)? (It suffices to say the name of the distribution with appropriate parameter(s).) (ii) What...
AP-Stats-2005-Q2 2. Let the random variable X represent the number of telephone lines in use by the technical support center of a manufacturer at noon each day. The probability distribution of X is shown in the table below P(x) 0.35 0.20 0.15 0.15 0.10 0.05 ) Suppose you come by every day at noon to see how many lines are in use. What are the chances that you don't find all 5 in use until your 7" visit? ) Find...
1. Suppose that random variables X and Y are independent and have the following properties: E(X) = 5, Var(X) = 2, E(Y ) = −2, E(Y 2) = 7. Compute the following. (a) E(X + Y ). (b) Var(2X − 3Y ) (c) E(X2 + 5) (d) The standard deviation of Y . 2. Consider the following data set: �x = {90, 88, 93, 87, 85, 95, 92} (a) Compute x¯. (b) Compute the standard deviation of this set. 3....
(a)Suppose X ∼ Poisson(λ) and Y ∼ Poisson(γ) are independent, prove that X + Y ∼ Poisson(λ + γ). (b)Let X1, . . . , Xn be an iid random sample from Poisson(λ), provide a sufficient statistic for λ and justify your answer. (c)Under the setting of part (b), show λb = 1 n Pn i=1 Xi is consistent estimator of λ. (d)Use the Central Limit Theorem to find an asymptotic normal distribution for λb defined in part (c), justify...