An urn contains three quarters, six dimes, and two pennies. (a) Randomly pick a coin from the urn and let X1 denote its value in cents. Compute E(X1) and V ar(X1). (b) Let X1, X2, . . . , Xn be a random sample with replacement from this urn. Let X¯ = (1/n) SUMMATION from k=1 to n, Xk. Compute E(X¯) and V ar(X¯).

An urn contains three quarters, six dimes, and two pennies. (a) Randomly pick a coin from the urn and let X1 denote its value in cents. Compute E(X1) and V ar(X1). (b) Let X1, X2, . . . , Xn be a random sample with replacement from this urn. Let X¯ = (1/n) SUMMATION from k=1 to n, Xk. Compute E(X¯) and V ar(X¯).

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Topic: Relationship of Two Variables: Scatterplot, Linear Correlation and Degree of Determination Suppose that data on a random sample of used cars of the same brand and model on mileage (in kilometers) and prices (in pesos) were collected and tabulated, as shown below. Price (in Mileage (in km) pesos) ху x2 (x1000) (x 10,000) 50 50 45 55 60 45 38 55 28 60 29 60 51 50 40 55 100 30 72 38
Cov(X,Y) 1) The correlation of two random variables X and Y, usually written as p(X,Y)= Var (X)Var (Y) where Cov(...) is the covariance and Var(.) is the variance of random variables. Let X be a uniform random variable on the interval [0; 1], and let Y = X2. Find the correlation between X and Y.
Show work! Let Xn be a random variable and mn be a median of Xn, n =1,2,.... Show that if Xn →d X for a random variable X,thenany limit point of mn is a median of X.
Suppose that: X~N(u,o²), if P(X < 85) = 0.9332, and P(X < 80) = 0.8413. Then find: the mean and the variance of thic distrihution? O 70 and 10 O 35 and 100 O 70 and 100 O 35 and 10
if x1, x2, ..., Xn be a random sample from Bin(4,0). is T = x UMVUE ? Justify your answer.
Let the following simple random sample X1, X2, · · , X11 following: 1. Binomial pmf. (11, ¾); 2. Uniform pmf; 3. Uniform pdf (0, a); 4. Exponential pdf with (µ). Find the corresponding pmf/pdf of Y1 , Y4, Y7 and F(Y;) where Yi < Y½ < .. < Y6 < ..< Yı1.
A time series {yt} follows an MA(2) model: Yt = 2 + Ut +0.54t-1 + 0.4ut-2. Assume that ut is a white noise series with a mean of O and a variance of 2. Please calculate Var(yt) (i.e. the variance of) 2.96 1.41 2.82 O 1.98
Suppose a simple random sample of size n equals 1000 is obtained from a population whose size is N equals 2 comma 000 comma 000 and whose population proportion with a specified characteristic is p equals 0.75. Complete parts (a) through (c) below.
b) Sketch the probability mass function and the cumulative distribution function of X (c) Consider a random sample of 6 parcels. If Y is the number of parcels taking longer than 1 day to arrive, write down the distribution of Y and its mean and variance.
The time between successive requests to a server are independent random variables, each exponentially distributed with mean 2 (so parameter 1/2). Let Tn denote the time of the nth request. What are the mean and variance of Tn? 2, n On, n² ● 2n, 4n 2n, 4n² None of the other choices.
Economics Now suppose that the time series process {Xt}, is expressed as Xt = z + et where et is iid with a mean of zero and a variance of σ , and the variable z does not change over time (time invariant) which means it has a mean E(z) = 0 and , and it is assumed that z and et are uncorrelated: i. Find the mean xt , E(Xt) and the variance Xt, var(Xt). Do they depend on t? ii. Determine the covariance of xt and xt+h for h > 0, Cov(Xt , xt+h) iii. Is xt stationary? Explain.
1.STATISTICAL INFERENCE