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Statistics and Probability
A sample of N=9 scores has a mean of M=20. One of the scores is changed and the new mean is found to be 22. If the score was originally X=7, what is its new value.
Statistics and Probability
Suppose that we have a fuse box containing 20 fuses, of which 5 are defective. If 2 fuses are
selected at random and removed from the box in succession without replacing the first, what is
the probability that both fuses are defective?
selected at random and removed from the box in succession without replacing the first, what is
the probability that both fuses are defective?
Statistics and Probability
Let N = 96000. From the intermittent signal 8:R
→
, we take samples -
10
where ke
EZ
. Under what conditions can the signal s be restored
from its samples? Also calculate this return formula
s(t) = . . .
→
, we take samples -
10
where ke
EZ
. Under what conditions can the signal s be restored
from its samples? Also calculate this return formula
s(t) = . . .
Statistics and Probability
Suppose you have 9 different (distinguishable) coins, and 4 different (distinguishable) juke- box slots.
- How many ways can you insert the 9 coins into the jukebox slots, if the order in which the coins are inserted does not matter?
- How many ways can you insert the 9 coins into the jukebox slots, if the order in which the coins are inserted into each jukebox does matter?
- How many ways can you insert 6 of the coins into one of the jukebox slots, if the order in which the coins are inserted matters?
Statistics and Probability
Throw a rock 10 times into a hat from different distances, like every 3 feet. The distances are the independent variable. The number of times that the rock lands in the hat is the dependent variable. Create a scatter plot of your data. Then add a linear trendline to the graph. Now add the equation of the trendline and the R squared value in the graph. Now create a regression analysis using data analysis in excel. Copy the data graph and output of the regression analysis into the word document of your assignment . Now analyse the data. What does the data show you? Does the distance away from the hat affect he number of times that the rock lands in the hat? Compare the equation of the trendline in the graph to the output coefficients in the output of the regression analysis. Are they same?
Statistics and Probability
- The data shown below are the price (in £s) of a ticket for a sample of 25 music concerts. Find the mode, mean and the median for this data set.
- 27 22 63 65 20 45 47 33 96 55 12 45 54 48 73
- 8 89 58 19 43 15 17 94 37 21
Statistics and Probability
Albus Severus Potter, a Physics Major, is a prolific and a Math genius of this university. If it is known
that Albus’ IQ belongs to the upper 1% of the student population, what is his minimum IQ? (Assume
normal IQ distribution, mean = 110, standard deviation = 10)
that Albus’ IQ belongs to the upper 1% of the student population, what is his minimum IQ? (Assume
normal IQ distribution, mean = 110, standard deviation = 10)
Statistics and Probability
Choose a numberUfrom the interval [0,1] with uniform distribution.(a) Find the cumulative distribution and density for the random variableY= ln(U+ 1).(b) What is the range of values forY?(c) Show that the density you have found has the property that∫Ωf(y)dy= 1.(d) Suppose you are handed a data sample from some statistical survey. How would youdetermine whether the sample comes from a distribution with this density?Question 4:
Statistics and Probability
LetXbe a random variable whose cumulative distribution function isF(x) =P(X≤x).Themedianof a random variable is defined to be the numberx∗such thatF(x∗) =12; thatis,P(X≤x∗) =12andP(X > x∗) =12.(a) Calculate the median of an Exponential(λ) random variable.(b) IfX∼Exponential(λ), what isP(X≤E(X))?(c) There have been many psychology studies that say that people overestimate their ownintelligence. In particular, a recent one states that 65% of Americans believe that theyare “smarter than average”*. Others argue this makes no sense, and that 50% of thepopulation should be of below-average intelligence, and 50% are of above-average intel-ligence. What’s your opinion on these statements? Is it possible for 65% of people to besmarter than average?
Statistics and Probability
From past experience, a professor knows that the test score of a student taking her finalexam is a continuous random variable with meanμ= 75 and varianceσ2= 25.(a) Use Markov’s inequality to give an upper bound for the probability that a student’s testscore will exceed 85.(b) Use Chebyshev’s inequality to determine what can be said about the probability that astudent will score between 65 and 85.(c) How many students would have to take the exam to ensure, with probability at least0.95, that the classaveragewould be within 2 marks of 75? Assume that you can applythe Central Limit Theorem.(d) How accurate do you think Markov’s inequality and Chebyshev’s inequality are? Do youthink it’s worth using them in practice? Why or why not?
(d) Suppose you are handed a data sample from some statistical survey. How would you determine whether the sample comes from a distribution with this density?
(d) Suppose you are handed a data sample from some statistical survey. How would you determine whether the sample comes from a distribution with this density?
