A First Course in Probability
9th Edition
ISBN: 9780321794772
Author: Sheldon Ross
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 7, Problem 7.21TE
(a)
To determine
To compute: Value for
(b)
To determine
To find: Value of i minimizes and maximizes
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Let X be a continuous random variable with density f (x) = 24x-4 for x > 2.
Then E (X) is equal to
Let X be a (continuous) uniform random variable on the interval [0,1] and Y be an exponential random variable with parameter lambda. Let X and Y be independent. What is the PDF of Z = X + Y.
the popularity density function f(x) for a uniform random variable X defined over the interval [2,10] is?
Chapter 7 Solutions
A First Course in Probability
Ch. 7 - A player throws a fair die and simultaneously...Ch. 7 - The game of Clue involves 6 suspects, 6 weapons,...Ch. 7 - Gambles are independent, and each one results in...Ch. 7 - Prob. 7.4PCh. 7 - The county hospital is located at the center of a...Ch. 7 - A fair die is rolled 10 times. Calculate the...Ch. 7 - Suppose that A and B each randomly and...Ch. 7 - N people arrive separately to a professional...Ch. 7 - A total of n. balls, numbered 1 through n, are put...Ch. 7 - Consider 3 trials, each having the same...
Ch. 7 - Consider n independent flips of a coin having...Ch. 7 - A group of n men and n women is lined up at...Ch. 7 - A set of 1000 cards numbered 1 through 1000 is...Ch. 7 - An urn has m black balls. At each stage, a black...Ch. 7 - In Example 2h, say that i and j, ij form a matched...Ch. 7 - Let Z be a standard normal random variable, and,...Ch. 7 - A deck of n cards numbered 1 through n is...Ch. 7 - Cards from an ordinary deck of 52 playing cards...Ch. 7 - Prob. 7.19PCh. 7 - Prob. 7.20PCh. 7 - For a group of 100 people, compute a. the expected...Ch. 7 - How many times would you expect to roll a fair die...Ch. 7 - Urn I contains 5 white and 6 black balls, while...Ch. 7 - A bottle initially contains m large pills and n...Ch. 7 - Let X1,X2... be a sequence of independent and...Ch. 7 - If X1,X2,....Xn are independent and identically...Ch. 7 - If 101 items are distributed among 10 boxes, then...Ch. 7 - Prob. 7.28PCh. 7 - There are 4 different types of coupons, the first...Ch. 7 - If X and Y are independent and identically...Ch. 7 - Prob. 7.31PCh. 7 - Prob. 7.32PCh. 7 - If E[X]=1 and Var(X)=5, find a. E[(2+X)2]: b....Ch. 7 - If 10 married couples are randomly seated at a...Ch. 7 - Cards from an ordinary deck are turned face up one...Ch. 7 - Let X be the number of ls and F the number of 2s...Ch. 7 - A die is rolled twice. Let X equal the sum of the...Ch. 7 - Prob. 7.38PCh. 7 - Let X1,... be independent with common mean and...Ch. 7 - Prob. 7.40PCh. 7 - A pond contains 100 fish, of which 30 are carp. If...Ch. 7 - A group of 20 people consisting of 10 men and 10...Ch. 7 - Let X1,X2,...,Xn be independent random variables...Ch. 7 - Between two distinct methods for manufacturing...Ch. 7 - Prob. 7.45PCh. 7 - Consider the following dice game. as played at a...Ch. 7 - Prob. 7.47PCh. 7 - A fair die is successively rolled. Let X and Y...Ch. 7 - There are two misshapen coins in a box; their...Ch. 7 - The joint density of X and Y is given by...Ch. 7 - The joint density of X and Y is given by...Ch. 7 - A population is made up of r disjoint subgroups....Ch. 7 - A prisoner is trapped in a cell containing 3...Ch. 7 - Consider the following dice game: A pair of dice...Ch. 7 - Ten hunters are waiting for ducks to fly by. When...Ch. 7 - The number of people who enter an elevator on the...Ch. 7 - Suppose that the expected number of accidents per...Ch. 7 - A coin having probability p of coming up heads is...Ch. 7 - There are n+1 participants in a game. Each person...Ch. 7 - Each of m+2 players pays 1 unit to a kitty in...Ch. 7 - Prob. 7.61PCh. 7 - Prob. 7.62PCh. 7 - Prob. 7.63PCh. 7 - Type i light bulbs function for a random amount of...Ch. 7 - The number of winter storms in a good year is a...Ch. 7 - In Example 5c, compute the variance of the length...Ch. 7 - Prob. 7.67PCh. 7 - The number of accidents that a person has in a...Ch. 7 - Repeat Problem 7.73 when the proportion of the...Ch. 7 - Consider an urn containing a large number of...Ch. 7 - In problem ,suppose that the coin is tossed n...Ch. 7 - Suppose that in Problem 7.75, we continue to flip...Ch. 7 - In Example 6b, let S denote the signal sent and R...Ch. 7 - In Example 6c y)2].Ch. 7 - The moment generating function of X is given by...Ch. 7 - Let X be the value of the first die and Y the sum...Ch. 7 - The joint density of X and Y is given by...Ch. 7 - Prob. 7.78PCh. 7 - Successive weekly sales, in units of $1,000, have...Ch. 7 - Show that E[(Xa)2] is minimized at a=E[X].Ch. 7 - Suppose that X is a continuous random variable...Ch. 7 - Prob. 7.3TECh. 7 - Let X be a random variable having finite...Ch. 7 - Prob. 7.5TECh. 7 - Prob. 7.6TECh. 7 - We say that X is stochastically larger than Y,...Ch. 7 - Prob. 7.8TECh. 7 - A coin having probability p of landing on heads is...Ch. 7 - Let X1,X2,....Xn be independent and identically...Ch. 7 - Prob. 7.11TECh. 7 - Let X1,X2,... be a sequence of independent random...Ch. 7 - Prob. 7.13TECh. 7 - Prob. 7.14TECh. 7 - Prob. 7.15TECh. 7 - Prob. 7.16TECh. 7 - Prob. 7.17TECh. 7 - In Example 41 t, we showed that the covariance of...Ch. 7 - Show that X and Y are identically distributed and...Ch. 7 - Prob. 7.20TECh. 7 - Prob. 7.21TECh. 7 - Prob. 7.22TECh. 7 - Show that Z is a standard normal random variable...Ch. 7 - Prove the Cauchy-Schwarz inequality, namely,...Ch. 7 - Show that if X and Y are independent, then...Ch. 7 - Prove that E[g(X)YX]=g(X)E[YX].Ch. 7 - Prove that if E[YX=x]=E[Y] for all x, then X and Y...Ch. 7 - Prob. 7.28TECh. 7 - Let X1,...,Xn be independent and identically...Ch. 7 - Consider Example 4f, which is concerned with the...Ch. 7 - An urn initially contains b black and w white...Ch. 7 - For an event A, let IA equal 1 if A occurs and let...Ch. 7 - A coin that lands on heads with probability p is...Ch. 7 - For another approach to Theoretical Exercise 7.34,...Ch. 7 - The probability generating function of the...Ch. 7 - One ball at a time is randomly selected from an...Ch. 7 - Prob. 7.37TECh. 7 - Prob. 7.38TECh. 7 - The best quadratic predictor of Y with respect to...Ch. 7 - Use the conditional variance formula to determine...Ch. 7 - Let X be a normal random variable with parameters...Ch. 7 - It follows from Proposition 6.1 and the fact that...Ch. 7 - Show that for random variables X and Z,...Ch. 7 - Prob. 7.44TECh. 7 - Verify the formula for the moment generating...Ch. 7 - For a standard normal random variable Z, let...Ch. 7 - Prob. 7.47TECh. 7 - Prob. 7.48TECh. 7 - The positive random variable X is said to be a...Ch. 7 - Let X have moment generating function M(t), and...Ch. 7 - Use Table 7.2 to determine the distribution of...Ch. 7 - Show how to compute cov(X,Y) from the joint moment...Ch. 7 - Suppose that X1,...,Xn have a multivariate normal...Ch. 7 - If Z is a standard normal random variable, what is...Ch. 7 - Suppose that Y is a normal random variable with...Ch. 7 - Consider a list of m names, where the same name...Ch. 7 - Prob. 7.2STPECh. 7 - Prob. 7.3STPECh. 7 - Prob. 7.4STPECh. 7 - Prob. 7.5STPECh. 7 - Prob. 7.6STPECh. 7 - Prob. 7.7STPECh. 7 - Prob. 7.8STPECh. 7 - Prob. 7.9STPECh. 7 - Prob. 7.10STPECh. 7 - Prob. 7.11STPECh. 7 - Prob. 7.12STPECh. 7 - Prob. 7.13STPECh. 7 - Prob. 7.14STPECh. 7 - Prob. 7.15STPECh. 7 - Prob. 7.16STPECh. 7 - Prob. 7.17STPECh. 7 - Prob. 7.18STPECh. 7 - There are n items in a box labeled H and m in a...Ch. 7 - Let X be a nonnegative random variable having...Ch. 7 - Let a1,...,an, not all equal to 0, be such that...Ch. 7 - Prob. 7.22STPECh. 7 - Prob. 7.23STPECh. 7 - Prob. 7.24STPECh. 7 - Prob. 7.25STPECh. 7 - Prob. 7.26STPECh. 7 - Prob. 7.27STPECh. 7 - Prob. 7.28STPECh. 7 - Prob. 7.29STPECh. 7 - Prob. 7.30STPECh. 7 - Prob. 7.31STPECh. 7 - Starting with etX=1+tX+t2X22!+t3X33!+...+tnXnn!...
Knowledge Booster
Similar questions
- 1) Let x be a uniform random variable in the interval (0, 1). Calculate the density function of probability of the random variable y where y = − ln x.arrow_forwardLet X be a continuous random variable with density function(x) = 4 1. Determine F(5) 2. Determine p(1arrow_forwardLet X and Y random variables have independent Gamma distributions with X-Gamma(1, 6) and Y-Gamma(2, B). a. Find the joint probability density of Z, = X + Y, Z, = X+Y a. Find the marginal pdf of Z2.arrow_forwardLet the probability density function of the random variable X is x f(x) Then Mx (t) is 0 , x = 1,2,3,... , otherwisearrow_forwardSuppose that X and Y are independent and uniformly distributed random variables. Range for X is (−1, 1) and for Y is (0, 1). Define a new random variable U = XY, then find the probability density function of this new random variable.arrow_forwardLet x be a random variable with a density function I (2) = { "0, 6x (1 – a), 0 < x < 1 elsewhere By finding the fırst and second moments, calculate the variance of x [1] (answer correct to 1 dp)arrow_forwardSuppose that X, Y , and Z are random variables with a joint density f(x, y, z) = ( 6/((1+x+y+z)^4)) , when x, y, z > 0, and 0, otherwise. Determine the distribution of X + Y + Z.arrow_forwardLet X1, X2, . X6 be an i.i.d. random sample where each X, is a continuous random variable with probability density function f(x) = e-(-0) , x > 0 Find the probability density function for X(6).arrow_forward• Find the density of Z = (X+ Y)2, where X and Y are independent uniform random variables over (-1, +1).arrow_forwardLet Y1 and Y2 denote the proportions of two different types of components in a sample from a mixture of chemicals used as an insecticide. Suppose that Y1 and Y2 have the joint density function given by 2, 0syı s 1, 0 < y2 < 1, 0 < y1 + y2 < 1 0, elsewhere fV1,y2) = (Notice that Y1+Y2 < 1 because the random variables denote proportions within the same sample.) Find P(Y1 < 3/4, Y2 < 3/4) P(Y1 < 1/2, Y2 < 1/2)arrow_forwardThe life lengths of two transistors in an electronic circuit is a random vector (X; Y) where X is the life length of transistor 1 and Y is the life length of transistor 2. The joint probability density function of (X; Y) is given by x 2 0, y 2 0 fx.,fx.v) = 20 else Then the probability that the first transistor burned during half hour given that the second one lasts at least half hour equals Select one: a. 0.606 b. 0.3935 C. 0.6318 d. 0.3669 e. 0.7772arrow_forwardc) Let Y₁, Y₂,..., Yn be a random sample whose probability density function is given by f(v:B)= 684 - fa 00 0, elsewhere 200 200 200 and suppose that n = 200, y = 20, y = 100, y = 250 and $ = 0.025. i=1 i) Derive the standard error of ß, se(B) = 0.0009, using MLE approach. ii) Find an approximate 95% Confidence interval for B.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:9780134753119
Author:Sheldon Ross
Publisher:PEARSON