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Suppose the probability density of X is given by
f(x) = {(kxe)^(-x^2), X>0
=0, Otherwise
(a) find the value of k.
(b) find the distribution function of X, i.e., the cumulative density function of X.
Let p, q, and r be the propositions
p: You get an A on the final exam.
q: You do every exercise in this book.
r: You get an A in this class.
Write these propositions using p, q, and r and logical connectives (including negations).
1. You get an A on the final, you do every exercise in this book, and you get an A in this class.
2. To get an A in this class, it is necessary for you to get an A on the final.
3. You get an A on the final, but you don’t do every exercise in this book; nevertheless, you get an A in this class.
4. Getting an A on the final and doing every exercise in this book is sufficient for getting an A in this class.
Let p, q, and r be the propositions
p: You have the flu.
q: You miss the final examination.
r: You pass the course.
Express each of these propositions as an English sentence.
p → q
¬q ↔ r
q →¬ r
p ∨ q ∨ r
(p → ¬r) ∨ (q → ¬r)
Let p, q, and r be the propositions
p: You have the flu.
q: You miss the final examination.
r: You pass the course.
Express each of these propositions as an English sentence.
p → q
Show, by the use of replacement rules, that (-p ^ q) ^ (q→p) = F
are logically equivalent.
A poll is given, showing 35% are in favor of a new building project.
If 9 people are chosen at random, what is the probability that at least 5 of them favor the new building project?
Probability = (Please show your answer to 4 decimal places)
Suppose that about 77% of graduating students attend their graduation. A group of 33 students is randomly chosen, and let X be the number of students who attended their graduation.
- What is the distribution of X? X ~
- ? B U N
- (,)
- Please show the following answers to 4 decimal places.
- What is the probability that exactly 25 number of students who attended their graduation in this study?
- What is the probability that less than 25 number of students who attended their graduation in this study?
- What is the probability that at most 25 number of students who attended their graduation in this study?
- What is the probability that between 20 and 26 (including 20 and 26) number of students who attended their graduation in this study?
the researchers believes that the non-smoker children is taller than the smoker one.test this claimusing the standard deviation of 0.01
A poll is given, showing 80% are in favor of a new building project.
If 7 people are chosen at random, what is the probability that fewer than 5 of them favor the new building project?
Probability = (Please show your answer to 4 decimal places)
Assume Binomial Distribution with n = 10 and p = 0.6. Please show your answers to 4 decimal places.
P(X = 4) =
P(X ≤ 4) =
P(X < 4) =
P(X >4) =
P(X ≥ 4) =
