# STAT 100A If the ? 2 of a random variable could be random

Question 1Not yetansweredMarked out of1.00 If the ? 2 of a random variable could be random (it is not, the way we studied probability, but suppose it was) whatdistribution would be the most suitable possible candidate for it?Select one:a. A normal distributionb. A Gamma distributionc. A bernoulli distribution Question 2Not yetanswered Suppose that a surveyor is trying to determine the areas of a rectangular eld, in which the measured length X and themeasured width Y are independent random variables that uctuate widely about the true values, according to the followingprobability distributions for X and for Y. Marked out of1.00 X P(X) Y P(Y)— —- —- —- 8 1/4 4 1/210 1/4 6 1/211 1/2 The calculated area A=XY of course is a random variable. What is the expected area? Select one:a. 10b. 0c. 50d. 35 Question 3Not yetansweredMarked out of1.00 Let X be the cosine of the angle at which electrons are emitted in muon decay. X is a random variable with the followingdensity 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 nn = ? i=1 n Xi . Which one has the smallest standard deviation? Select one:a. W has the smallest standard deviationb. Y has the smallest standard deviationc. Both have the same standard deviationd. Both X and Y are constants https://ccle.ucla.edu/mod/quiz/attempt.php?attempt=1213769 1/6 11/26/2016Question 4Not yetansweredMarked out of1.00 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 exactlyone request for a song. All of their requests are made independently. Assume that each person asks for a pop song withprobability 0.37, a rock song with probability 0.2, or a rap song with probability 0.43. What is the probability that 50 ormore requests are made for pop songs? Select one:a. 0.37b. 0.63c. 0.146d. 1.06 Question 5Not yetanswered A lot acceptance sampling plan for large lots calls for sampling 50 items and accepting the lot if the number ofnonconformances is no more than 5. Showing work, nd the approximate probability of acceptance if the true proportion ofnonconformances in the lot is 10% Marked out of1.00 Select one:a. 0.0386b. 0.5c. 0.00045d. 0.6 Question 6Not yetansweredMarked out of1.00 Consider the bivariate normal distribution2 x ? ?x1[()????? exp{?22?x2(1 ? ? )2??x ?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 functionb. The marginal distribution of X multiplied by the marginal distribution of Yc. A multinomial distributiond. 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 7Not yetanswered Mass screening the whole population to determine the proportion of people who suffer from a disease with prevalence lessthan 1 per hundred thousand may not be a good idea due to which of the following problems? Marked out of1.00 Select one:a. The conditional probability that a screened individual has the disease given that the screening test is positive is veryhigh. It could create a panic.b. The conditional probability that a screened individual has the disease given that the screening test is positive is verylow. 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 11/26/2016Question 8Not yetansweredMarked out of1.00 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 withparameter ? 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 thatwould maximize the joint density function.Which is that value? Select one: Question 9Not yetansweredMarked out of1.00 ? (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 February1998, 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 10Not yetanswered Choose…Choose… Let X and Y be two random variables. Let a,b,c,d be constants. The correlation between the random variablesW=a+bX and T=c-dY, ?(W , T ), is equal to (choose one). Marked out of1.00 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 11/26/2016Question 11Not yetansweredMarked out of1.00 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. ?xi=1n xi b. 0¯c. 2x d. 1 Question 12 The covariance of random variable X with itself is Not yetanswered Select one: Marked out of1.00 a. The variance of Xb. 0c. 1d. twice the standard deviation of X Question 13Not yetanswered A television store owner gures that 45 percent of the customers entering his store will purchase an ordinary televisionset, 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 of1.00 Select one:a. 0.00486b. 0.0675c. 0.321d. 0.11664 https://ccle.ucla.edu/mod/quiz/attempt.php?attempt=1213769 4/6 11/26/2016Question 14Not yetansweredMarked out of1.00 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 expressionlog 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 3i ) +. . .) ? 12 ( t 2 3 2n t + 2 3 3!n E (z 3i ) +. . .) +] 2 2 = [( t 2 2 3 t + 1 3!n E (z 3i ) +. . .) ? 12 n( 2 t 2 2n 3 + t 3 3!n E (z 3i ) +. . .) +] 2 As n goes to in nity,Select one:2 a. that expression goes to t 2 b. that expression goes to 0c. that expression equals the moment generating function of a N (?, ?)d. that expression goes to in nity Question 15Not yetansweredMarked out of1.00 The length of a phone call, X, in minutes, is a random variable that can be modeled by an exponential distribution withexpected value 10 in minutes.Match the probability models that must be used to nd the probabilitiesf (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 yetanswered ? Marked out of1.00 10 2 cos(2?x )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 manyvalues 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 11/26/2016Question 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 yetansweredMarked out of1.00 Select one:a. 1/y,b. N (? y ? [1, e] = 1/2, ? 2 = 1/12) c. exponential with lambda=1. Question 18Not yetansweredMarked out of1.00 Suppose X i , ivariance ? 2 = 1, . . . n are independent and identically distributed random variables with expected value ? and Then ? E[ i=1 ¯)(x i ?x 2 n?1 equalsSelect one:2¯a. nx b. ? 2¯/n ? 1c. x ¯d. (n ? 1)x https://ccle.ucla.edu/mod/quiz/attempt.php?attempt=1213769 6/6