11/26/2016 Fall 2016 Homework 12Due Thursday 12/1, before 8 PM. Must submit before 8PM. My sites / 16F-STATS100A-1 / HOMEWORK / Fall 2016- Homework 12-Due Thursday 12/1, before 8 PM. Must submit before 8PM. Control Panel Question 1 Not yet answered Marked out of 1.00 If the 2 of a random variable could be random (it is not, the way we studied probability, but suppose it was) what distribution would be the most suitable possible candidate for it? Select one: a. A normal distribution b. A Gamma distribution c. A bernoulli distribution Question 2 Not yet answered Suppose that a surveyor is trying to determine the areas of a rectangular eld, in which the measured length X and the measured width Y are independent random variables that uctuate widely about the true values, according to the following probability distributions for X and for Y. Marked out of 1.00 X P(X) Y P(Y) --- ---- ---- ---- 8 1/4 4 1/2 10 1/4 6 1/2 11 1/2 The calculated area A=XY of course is a random variable. What is the expected area? Select one: a. 10 b. 0 c. 50 d. 35 Question 3 Not yet answered Marked out of 1.00 Let X be the cosine of the angle at which electrons are emitted in muon decay. X is a random variable with the following density function. f (x) = 1+X , 2 1 x 1, 1 < < 1 Let X 1 , X 2 , . . . . , X n be n independent and identically distributed random variables with the density given above each. Consider now the following functions (i) Y n = (ii ) W 3 Xi i=1 n n = i=1 n Xi . Which one has the smallest standard deviation? Select one: a. W has the smallest standard deviation b. Y has the smallest standard deviation c. Both have the same standard deviation d. Both X and Y are constants https://ccle.ucla.edu/mod/quiz/attempt.php?attempt=1213769 1/6 11/26/2016 Question 4 Not yet answered Marked out of 1.00 Fall 2016 Homework 12Due Thursday 12/1, before 8 PM. Must submit before 8PM. A certain DJ takes requests for songs at a party. Assume that there are 120 people at the party, each of whom makes exactly one request for a song. All of their requests are made independently. Assume that each person asks for a pop song with probability 0.37, a rock song with probability 0.2, or a rap song with probability 0.43. What is the probability that 50 or more requests are made for pop songs? Select one: a. 0.37 b. 0.63 c. 0.146 d. 1.06 Question 5 Not yet answered A lot acceptance sampling plan for large lots calls for sampling 50 items and accepting the lot if the number of nonconformances is no more than 5. Showing work, nd the approximate probability of acceptance if the true proportion of nonconformances in the lot is 10% Marked out of 1.00 Select one: a. 0.0386 b. 0.5 c. 0.00045 d. 0.6 Question 6 Not yet answered Marked out of 1.00 Consider the bivariate normal distribution 2 x x 1 [( ) exp{ 2 2 x 2(1 ) 2x y 1 1 f (x, y) = y y + ( 2 ) y y x x 2 ( y )( x )]} y < x < , < y < When we make = 0 we get Select one: a. A bivariate gamma density function b. The marginal distribution of X multiplied by the marginal distribution of Y c. A multinomial distribution d. The product of the conditional distribution for Y (which is normal) and the marginal distribution of X. e. The product of the conditional distribution of Y and the conditional distribution of X Question 7 Not yet answered Mass screening the whole population to determine the proportion of people who suffer from a disease with prevalence less than 1 per hundred thousand may not be a good idea due to which of the following problems? Marked out of 1.00 Select one: a. The conditional probability that a screened individual has the disease given that the screening test is positive is very high. It could create a panic. b. The conditional probability that a screened individual has the disease given that the screening test is positive is very low. It could be nancially very expensive. c. The conditional probability that the screening test is positive given that the person has the disease is very high. d. The conditional probability that the test is positive given that the person does not have the disease is very low. https://ccle.ucla.edu/mod/quiz/attempt.php?attempt=1213769 2/6 11/26/2016 Question 8 Not yet answered Marked out of 1.00 Fall 2016 Homework 12Due Thursday 12/1, before 8 PM. Must submit before 8PM. Consider a random sample of size n (i.e, a set of i.i.d. r.v. X_1, X_2,......, X_n) from a two-parameter distribution with parameter unknown and parameter known. The density function of X i , i = 1, . . . , n is f (xi 1 , ) = exp{ x }, < x Find the joint density function f(x_1, ..., x_n) and then maximize that function to obtain the value of the theta parameter that would maximize the joint density function. Which is that value? Select one: Question 9 Not yet answered Marked out of 1.00 (x i ) a. = b. = /n c. = n d. = n i n xi i i xi In the USA Today of February 20th, it said that \"Tiger Woods has not missed a cut since the Buick Invitational in February 1998, a string of 63 consecutive events. While Woods' streak is only fth best all the time, it is the longest active streak.\" (USA Today, 2/20/2001, page 1C). Say whether each of the following statements is true or false or can not be determined. The law of averages says that situations like that described for Tiger can't happen. Tiger will not miss a cut in the next event, since his luck is hot. Question 10 Not yet answered Choose... Choose... Let X and Y be two random variables. Let a,b,c,d be constants. The correlation between the random variables W=a+bX and T=c-dY, (W , T ), is equal to (choose one). Marked out of 1.00 Select one: a. abC ov(X,Y ) V ar(X)V ar(Y ) bdC ov(X,Y ) b. 2 b V ar(X)d 2 V ar(Y ) c. (X, Y ) bdC ov(X,Y ) d. 2 2 a V ar(bX)c V ar(dY ) https://ccle.ucla.edu/mod/quiz/attempt.php?attempt=1213769 3/6 11/26/2016 Question 11 Not yet answered Marked out of 1.00 Fall 2016 Homework 12Due Thursday 12/1, before 8 PM. Must submit before 8PM. Let X 1 , X 2 , . . . . , X n be i.i.d. random variables. n i=1 ) (xi x equals Select one: + a. x i=1 n xi b. 0 c. 2x d. 1 Question 12 The covariance of random variable X with itself is Not yet answered Select one: Marked out of 1.00 a. The variance of X b. 0 c. 1 d. twice the standard deviation of X Question 13 Not yet answered A television store owner gures that 45 percent of the customers entering his store will purchase an ordinary television set, 15 percent will purchase a plasma television set, and 40 percent will just be browsing. If 5 customers enter his store on a given day, what is the probability that he will sell exactly 2 ordinary sets and 1 plasma set on that day? Marked out of 1.00 Select one: a. 0.00486 b. 0.0675 c. 0.321 d. 0.11664 https://ccle.ucla.edu/mod/quiz/attempt.php?attempt=1213769 4/6 11/26/2016 Question 14 Not yet answered Marked out of 1.00 Fall 2016 Homework 12Due Thursday 12/1, before 8 PM. Must submit before 8PM. In the mathematical proof of the CLT, we nd the following expression log Mn (t) = n log(1 + x) = n (x x 2 + 2 x 3 3 . . . .) 2 = n [( t 2 2n 3 t + 3 3!n E (z 3 i ) +. . .) 1 2 ( t 2 3 2n t + 2 3 3!n E (z 3 i ) +. . .) +] 2 2 = [( t 2 2 3 t + 1 3!n E (z 3 i ) +. . .) 1 2 n( 2 t 2 2n 3 + t 3 3!n E (z 3 i ) +. . .) +] 2 As n goes to in nity, Select one: 2 a. that expression goes to t 2 b. that expression goes to 0 c. that expression equals the moment generating function of a N (, ) d. that expression goes to in nity Question 15 Not yet answered Marked out of 1.00 The length of a phone call, X, in minutes, is a random variable that can be modeled by an exponential distribution with expected value 10 in minutes. Match the probability models that must be used to nd the probabilities f (x) = 0.1e 0.1x N ( = 10, 2 Choose... Choose... = 0.0001) Choose... Gamma( = 0.1, = 3) Question 16 One of the uses of random numbers is to solve mathematical integrals such as the following Not yet answered Marked out of 1.00 1 0 2 cos(2x )dx Note: the function inside the integral is not a density function. Which of the following random variables would allow us to solve the integral by simulating many values of that random variable and taking the average of all the simulated values? Select one: a. The Uniform(0,1) b. The Exponential( ) = 1 c. The Normal(0,1) d. The Bernoulli with p=0.1 https://ccle.ucla.edu/mod/quiz/attempt.php?attempt=1213769 5/6 11/26/2016 Question 17 Fall 2016 Homework 12Due Thursday 12/1, before 8 PM. Must submit before 8PM. If X is uniformly distributed over (0,1), nd the density function of Y = e x . Not yet answered Marked out of 1.00 Select one: a. 1/y, b. N ( y [1, e] = 1/2, 2 = 1/12) c. exponential with lambda=1. Question 18 Not yet answered Marked out of 1.00 Suppose X i , i variance 2 = 1, . . . n are independent and identically distributed random variables with expected value and The n E[ i=1 ) (x i x 2 n1 equals Select one: 2 a. nx b. 2 /n 1 c. x d. (n 1)x https://ccle.ucla.edu/mod/quiz/attempt.php?attempt=1213769 6/6