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Independence of complements. Show that if events A and B obey the multiplication rule, P(A and B) = P(A)P(B), then A and the complement Bc of B also obey the multiplication rule, P(A and Bc) = P(A)P(Bc). That is, if events A and B are independent, then A and Bc are also independent.
Mendelian inheritance. Some traits of plants and animals depend on inheritance of a single gene. This is called Mendelian inheritance, after Gregor Mendel (1822-1884). Exercises 5.36 to 5.39 are based on the following:
Each of us has an ABO blood type, which describes whether two characteristics called A and B are present. Every human being has two blood type alleles (gene forms), one inherited from our mother and one from our father. Each of these alleles can be A, B, or O. Which two we inherit determines our blood type. Here is a table that shows what our blood type is for each combination of two alleles:
Alleles inherited
Blood Type
A and A
A
A and B
AB
A and O
B and B
B
B and O
O and O
O
We inherit each of a parent's two alleles with probability 0.5. We inherit independently from our mother and our father.
What is the probability that exactly two accidents will occur in a particular two-day interval? What is the probability that one will have to wait at least two days to observe the next two accidents.
You are interested in using linear regression to test whether drinking a protein shake improves weightlifting performance. From a sample of 200 college students, you estimate a linear regression with WEIGHTLIFT as the dependent variable and PROTEI..
What is the probability of getting seven heads in a sample of twenty coin flips? Is this significantly different from the population in which P = 0.50 if the alpha is 0.05?
a patient receiving a yearly physical examination and must have 16 checks or tests performed. the sequence in which the
In the current year, Andrew received a gift of property from his uncle. At the time of the gift, the property had a FMV of $114,000 and an adjusted basis to his uncle of $70,000. After deducting the annual exclusion, the amount of the gift was $10..
When testing for the difference between the variances of two population with sample sizes of n1=8 and n2=10, the number of degrees of freedom are?
for a population with micro 40 and s 7 find the -score for each of the following x values. note you probably will need
which of the following statements regarding a negative correlation is true?a. high values of the x variable tend to be
the following data represent the amount of sugar consumed in lbs. in a household during five randomly selected weeks.
a gardener has 1000 square yards of land available to devote to cash crops. profits expected by crop are 20 per square
Also, if the standard deviation of all pumps σ is unknown, is there an easier formula to estimate the sample size to control the width of the confidence interval? Please explain it.
Bristowe has asked for your advice in evaluating the current phone reservation system. Create a simulation model to investigate her concerns. Make recommendations about the reservation agents.
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