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The same six testers rated the taste of two ice creams. Taste ratings are not normally distributed, so a t-test should not be done.Is there a significant difference in the ratings of the two ice crea
Consider two independent random variables Xsub1 and Xsub2 having the same Cauchy distribution f(x)=1/(pie(1+x^2)) for negative infinity <x < positive infinity.
Obtain the general solution of a non-homogeneous ODE y'''+2y''-5y'-6y=100e^3x + 18e^-x. Verify your solutions using MATLAB.
Determine the area under the standard normal curve that lies between (a) Z = -0.83, and Z = 0.83 (b) Z = - 1.35 and Z = 0, (c) Z = -1.38, and Z = 0.63.
Determine the area under the standard normal curve in parts (a) through (c) below. Find the area under the normal curve to the left of z = 1 plus the area under the normal curve to the right of z =
Determine the area under the standard normal curve that lies to the left of (a) Z=1.02, (b) = -0.11, (c) Z = -1.58, and (d) Z = -0.43.
When constructing and implementing hypothesis tests, what reasoning is used behind the statement of the null and alternative hypotheses?
Let S = {a, b, c} be a sample space. Suppose P is a probability on S and that you know P({a}) = 0.2 and P({a, b}) = 0.5 Then what are P({b}) and P({c})? Explain how you know.
During an assembly process, parts arrive just as they are needed. However, at one station, the probability is 0.01 that a defective part will arrive in a one-hour period. Find the probability that
Let G be a set and let * be an associative binary operation on G. Assume that there exists a left identity element in G and that every element in G has a left inverse. Prove that (G, *) is a group.
Which of the following is true for a symmetrical distribution?
Suppose that X and Y are independent exponential random variables each with rate ?. What is the conditional probability of X, given that Z = X + Y = z?
When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Let X = the number of defective boards in a random sample of size? = 25.
Consider a simple card game where there are four cards labeled 1, 2, 3, and 4. Each round, my friend first draws a card randomly from the four. After my friend draws the card, I also randomly draw a
The bank opens at 8am and you arrive at the bank at uniformly random time between 8am and 9am. Let X be the number of people who entered the bank before you. Find the expectation and the variance of
Find E(X) and Var(X). What is the probability of no defective product, the probability of at least one faulty product and find probability of at least three defective products. Calculate the probab
Let Xsub1 and Xsub2 be two continous random variables having the joint probability density
Use the distribution function techniques to find the probability density of the amount that the service station has left in its tanks at the end of the day
Consider two components whose lifetimes X and Y are independent and exponentially distributed with parameters lambda_x and lambda_y, respectively. Find the joint pdf of total lifetime X+Y and the p
An instructor stated at the beginning of a course that on the average 35% of students do not pass the exam. After the exam, a random sample of 100 students who took the exam was selected, and 25 of
If the above confidence interval is used to test the given hypotheses, what would the statistical decision be ? What would the level of significance of the hypothesis test be?
The Florida Fruit Supply Company uses bottles that are labeled as containing 23 oz of orange juice. A random sample of 24 such bottles shows that the sample mean and standard deviation are 22.75 oz
List the steps you would follow to determine the reliability of the exam. About 100 students will take this exam. The exam will take 90 minutes, which is the full length of the exam period. There
Hint: Show that Mzn(t)=exp(-sqr(n)*t - ln(1-t/sqr(n))) and then use the expansion ln(1-s)=-s-(1+E)s^2/2 where E->0 as s->0. Does the above limiting distribution also follow as a result of the
Show that Yn=e^(-Xnbar)converges stochastically to P[X=0]=e^-u. Find the assymptotic normal distribution of Yn.