Suppose we fit a SLR model where y-hat = Beta 0 hat + Beta 1 hat(x1), but the response is affected by a 2nd variable X2 such that a true regression function is E[y] = Beta 0 + Beta 1(X1) + Beta 2(X2). Find the bias of Beta 1 hat..
Suppose we flip a fair six times in a and second the six in the order they occur, using H for heads and T for tails. ("Fair" means that the probability of heads is exactly 1/2.) Below are two possible outcomes. We get the sequence HHHHHH We get the sequence.
Suppose we would like to test the usefulness of a drug for treating cancer.
We get a list of Stanford students who are receiving care for cancer at the Stanford Hospital and contact a random sample of 100 of them. Among them, 40 agree to participate in.
Suppose we have a random variable X following a normal distribution with a mean= 42.8 and standard deviation= 10.5
Find the 10th percentile
Note this is actually finding the constanct c such that P (X < c) = .10.
suppose we assume the following:
any CFCs released into the atmosphere remain there indefinitely
At current rates of release, atmospheric concentration of CFCs would double in 100 yrs.
Atmospheric release rate are, however, not constant but growing at 2%/yr.
.
Suppose with your new-found knowledge of probability, you have managed to
win the lottery and are celebrating by hiring a private yacht to sail you and your closest
friends around the Caribbean for a week. How many 7-day itineraries are possible if you
.
Suppose we want to be 90% condent of meeting an MTTF of at least 2,000,000 hours (in other words, a failure rate of 500 FITs). We can test for 2000 hours, and we want to allow for up to two fails. What sample size do we need? What is the.
Suppose we represent Pascal's triangle as a list, where item n is row n of the triangle. For example, Pascal's triangle to depth four would be given by list(c(1), c(1, 1), c(1, 2, 1), c(1, 3, 3, 1)) The n-th row can be obtained from n - 1 by adding.
Suppose we have two urns, Urn 1 and Urn 2. Urn 1 contains 7 red marbles and 11 white marbles. Urn 2 contains 9 red marbles and 13 white marbles. The experiment consists of first choosing an urn with equally likely probability, and then drawing a marble from that urn..
Suppose we flip a fair coin n times where n > 2 and consider the sample space of all possible coin toss sequences. • Let A be the event that the first flip is Tails. • Let B be the event that the first and second flips are the same..
Suppose we are given a system of linear equations. What are the advantages and disadvantages of using the substitution and elimination methods to solve the system? Provide examples..
Suppose we construct a 90% confidence interval for a mean. This is equivalent to a two-tailed hypothesis test with level of significance. Choose the correct answer below. 1% 5% 10% 20%.
"Suppose we have a weightd coin, which comes up heads with probability p. We toss the coin until we obtain a total of n heads (for some integer n>0). What is the expected number of tosses until the nth head?"
Can someone explain this to me IN.
Suppose we know that
f(upper bound=2) and (lower bound=1) f(x)dx=1
f(upper bound=8 and lower bound=4) f(x)dx=5
f(upper bound 8 and lower bound = 1) f(x)dx=2
a. What is f(upper bound=8 and lower bound=4) -7f(x)dx?
b..
Suppose we lived in a society without interest. At age 25, you begin putting $750 per month into a cookie jar until you retire at age 65. At age 65, you begin to withdraw $2500 per month from the cookie jar. How long will your retirement fund last?.
Suppose we define vector addition and scalar mulitplication of R2 as follows:
(v1, v2) + (w1, w2) = (0, v2+w2)
k(v1,v2) = (0, -kv2)
Please verify if Vector space by showing each axiom..Thank You.
Suppose we have the simple linear regression model: yi= beta 1+beta2Xi+ui Using a sample of size n = 20 observations, we obtain the OLS estimate b2 = 1.05 and its associated standard error,s. e. (b2) = 0.57. We want to test the null hypothesis, H0 : beta2 = 0 ,.
Suppose X = 8 and y = 7 in the figure, which is not drawn to scale. Find the following. Enter exact answers given as fractions, not decimal approximations. cos(theta) = sin(theta) = tan(theta) =.
Suppose we want to form three digit numbers in our system of counting numbers, that is, using the set digits {0,1,2,...8,9} (for example, 301 and 135 are such numbers but 024 is not)
(1) how many such numbers are possible?
(2) how many such.
Suppose we do a CI estimate of a population mean using sample means.
A) As sample sizes increase, what will happen to the margin of error? Explain
B) Will our point estimates of µ by x’s get better or worse as the sample size.
Suppose we toss a fair coin 200 times. Fill in the blanks: Use the Normal approximation to find the probability that the sample proportion is A) Between 0.4 and 0.6 is _____ (Give your answer to 4 decimal places). B) Between 0.45 and 0.55 is _____ (Give your answer to.
Suppose we are attending a college which has 3000 students. We wish to choose a subset of size 100 from the student body. Let X represent the subset, chosen using the following possible strategies. For which strategies would it be appropriate to assign the uniform distribution to X? If it.
Suppose we find x 2 and ya to be the proposed dimensions of a rectangle that minimize its area. What test should we use to ascertain that these dimensions produce the minimumum area? A (x) >0 A (r) <0 A (x) <0.
Suppose x = c1e^(-t) + c2e^(2t) 1) Verify that x = c1e^(-t) + c2e^(2t) is a solution to x''-1x'-2x=0 by substituting it into the differential equation. 2) Find x(t) if x(0)=3 and x'(0)=1.
Suppose we have a distribution of student exam scores on an easy test What measure of spread would be best to describe this data? A- The spread should be described the IQR because the distribution will be skewed to the left B. The spread should be described with tie standard.
Suppose we wish to interpolate n + 1 data points (n > 2) with a piecewise quadratic
polynomial. How many continuous derivatives at most can this interpolant be guaranteed
to have? Explain..
Suppose x = Ae^-t + Be^4t. a. Verify that x = Ae^-t + Be^4t is a solution to x -3x?-4x=0 by substitutinq it into the differential equation. (Enter the terms in the order given) + + =0 b. Find x(t) if x(0) = 4 and x?(0) = 2. x(t)= help(formulas).
Suppose we conduct a hypothesis test and the null hypothesis is H0: mu >= 45. What is the alternative hypothesis?
H1: mu < 50
H1: mu not = 45
H1: mu < 45
H1: mu > 45
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Suppose we want to do a study about lifestyle of students in the cafeteria, would the "students who order Diet Pepsi with lunch" constitute a random sample of students in the cafeteria? Explain your answer..
Suppose we are testing the hypotheses H0 :?= 100 and Ha:?< 100. Suppose the population variance is unknown. Which sample mean will have the smaller p-value, x = 90 or x = 85? Select all that apply.
a) x = 85 will have a smaller p-value because.
Suppose we were to take 100 random samples from a population, each of size 50. If we were to calculate a 99% confidence interval from each of those samples, how many of the intervals would we expect to have obtained the true parameter value?
A) 1
.
Suppose we perform a sequence of n operations on a data structure in which the ith operation costs i if i is an exact power of 3 and 3 otherwise. Use aggregate analysis to getermine the amortized cost per operation. Also, redo the problem using the accounting method of analysis..
Suppose we have a standard 52-card deck of playing cards and 5 cards are dealt to you. a). What is the chance that all cards are the same suit if the first two cards spades?
b). What is the chance that the cards can be arranged in.
Suppose we have the same setting as in problem 2 but with a different sample size. (a) Suppose the true population mean compression strength of cans with strawberry drink is mu_s, and of cans with cola is mu_c. Compute the 95% confidence interval for mu_s - mu_c. (b) We want.
Suppose we have two integers, n and m who prime power decompositions are as followed: Where the set of p starts with pi being the smallest prime number between n and m when they are decomposed, and pk is the largest prime between the integers n and m when they're.
Suppose we are given a set of n = 100 data points from X_i, ~ N(mu,sigma^2). Let sigma^2 = 4. Suppose the true value of mu = 5 anti we want to test the hypothesis against the alternative hypothesis We use the test statistic T = and reject Recall that.
Suppose we want to develop a model to predict selling price of houses based on assessed value. A sample of 10 recently sold single-family houses in a small western city is selected to study the relationship between selling price and assessed value Assessed value($000) Observation Selling Price ($000) 78.17 101.90.
Suppose we calculate t = 2.7 for an upper tailed test based on 23 degrees of freedom. We may say the following about the p-value It is less than 0.001 It is between 0.005 and 0.01 It is between 0.01 and 0.02 It is between 0.01 and 0.05.
Suppose we flip a fair coin twice and roll a six-sided die, find the sample space associated with this experiment. Let x be the number of heads plus the result of the roll. Find P(X=x) for each possible value of x..
Suppose we are interested in the amount of time college students spend on social networking sites: Facebook, MySpace, and Twitter. We know the amount of time each student spends on social networking sites follows a Normal distribution with mean 7.6 hours and standard deviation 2.2. In this study we examine.
Suppose we have two urns, Urn 1 and Urn 2. Urn 1 contains 11 red marbles and 13 white marbles. Urn 2 contains 9 red marbles and 7 white marbles. The experiment consists of first choosing an urn with equally likely probability, and then drawing a marble from that urn..
Suppose we have a population that does not follow the normal distribution. What minimum sample size we should select in order to have an approximately normal distribution (symmetric)? A. more than 10% of population size B. it is based on population standard deviation C. 20 D. 30.
Suppose W, X, and Y are independent normal random variables with common mean mu and known standard deviations 5,7,9 respectively. Let S = 3W + 2X + Y be the sum of the three random variables, we take one observation from W, one from X and one from Y. Call.
suppose we are told that a number has the following remainder
0 mod 10
2 mod 11
7 mod 19
we are also told that the number is greater than 0 and less than the product 10*19*11=2090. What's.
Suppose we want to test a null hypothesis that states the mean of the population equals zero. When should we reject the null hypothesis?
Test statistic is close to zero
Test statistic is a large negative or large positive value
Test.
