Question 2. Suppose we have a class list of n names and n email addresses for STAT 416. Randomlypermute the names on the list in such a way that all n! permutations are equally likely, while the emailaddresses do not change. Let X be defined as the number of names in the permuted list that are matchedwith the correct email address. What is E(X)?

Answered: Image /qna-images/answer/6a2d6ea0-b6b6-4ce4-a170-b5a240fbdfae.jpg

Answered: Question 2. Suppose we have a class…

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...

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1.Suppose that one word is to be selected at random from the sentence "THE GIRL PUT ON HER BEAUTIFUL RED HAT". If X denotes the number of letters in the word that is selected, (1) What is the value of E(X)? (2) What is the value of Var(X)?
Number of ChildrenTable 1 shows the number of women (per 1000) between 15 and 50 years of age who have been married grouped by the number of children they have had. Table 2 gives the same information for women who have never been married.1 Number of Children Women per 1000 0 162 1 213 2 344 3 182 4 69 5+ 32 Table 1 Women who have been married Number of Children Women per 1000 0 752 1 117 2 72 3 35 4 15 5+ 10 Table 2 Women who have never been married 1http://www.census.gov/hhes/fertility/data/cps/2014.html, Table 1, June 2014. Condition gt requires numbers instead of "null" and "0" (a) Without doing any calculations, which of the two samples appears to have the highest mean number of children? Women who have been marriedWomen who have never been married Which of the distributions appears to have the mean most different from the median? Women who have been marriedWomen who have never been married…
If S = {a,b,c} with P(a) = P(b) and P(c) = 0.24, find P(a). (Enter answer as a decimal with at least 2 correct decimal places)
3) A light fixture contains five lightbulbs. The lifetime of each bulb is exponentially distributed with mean 200 hours. Whenever a bulb burns out, it is replaced. Let T be the time of the first bulb replacement. Let Xi, i = 1, . . . , 5, be the lifetimes of the five bulbs. Assume the lifetimes of the bulbs are independent.
Teachers want to know which night each week their students are doing most of their homework. Most teachers think that students do homework equally throughout the week. Suppose a random sample of students were collected which shows that the Number of students doing their homework on SUN where 16 Number of students doing their homework on MON where 18 Number of students doing their homework on TUE where 12 Number of students doing their homework on WED where 18 Number of students doing their homework on THR where 8 Number of students doing their homework on FRI where 4 Number of students doing their homework on SAT where 3 What is the Test Statistics to test the Hull Hypothesis that students were doing their homework with equal frequencies (that is, they fit a uniform distribution) against the alternative Hypothesis that students prefer doing their homework on a particular day (that is, they do not fit a uniform distribution)?
Show that the average time till the first head is observed is y₁= p-¹, where p is the probability of getting a head each time the coin is tossed. Then find a closed form explicit solution to yn, the average time till n consecutive heads are observed for the first time.

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