Q25.If the records show that, the probability of failing (with grade F) this course is p,...

Q25.If the records show that, the probability of failing (with grade F) this course is p, what is the probability that at most 2 students out of 15 fail this course? {Hint: use binomial distribution}

Q26.If the records show that, the probability for a student to get a grade B this course is p, what is the probability that exactly 4 students out of 15 will have a grade B for the course? {Hint: use binomial distribution}

Q27.What is the probability of selecting a grade A student for the first time either in 2nd or 3rd selection?

DATA: A:11 B:2 C:1 D:0 F:1

Expert Solution

orchestra answered 2 years ago

Show that, for any events E and F, P(E ∪ F) = P(E) + P(F) −...

Show that, for any events E and F, P(E ∪ F) = P(E) + P(F) − P(E ∩ F). Only use the probability axioms and indicate which axiom you use where

Suppose that the probability of obtaining a particular grade in an undergraduate statistics course, is defined...

Suppose that the probability of obtaining a particular grade in an undergraduate statistics course, is defined by the following table: grade A B C D F probability .25 .35 .2 .15 .05 (a) Using the usual numerical values for the grades, define the corresponding random variable, X, and its probability mass function, p(x). (b) Calculate P(X ≤ 2), P(X < 2), and P(X ≥ 3). (c) Plot the cumulative distribution function F(x). (d) Compute the mean µ = E(X).

Suppose f : X → S and F ⊆ P(S). Show, f −1 (∪A∈F A) =...

Suppose f : X → S and F ⊆ P(S). Show, f −1 (∪A∈F A) = ∪A∈F f −1 (A) f −1 (∩A∈F A) = ∩A∈F f −1 (A) Show, if A, B ⊆ X, then f(A ∩ B) ⊆ f(A) ∩ f(B). Give an example, if possible, where strict inclusion holds. Show, if C ⊆ X, then f −1 (f(C)) ⊇ C. Give an example, if possible, where strict inclusion holds.

Let p and q be propositions. (i) Show (p →q) ≡ (p ∧ ¬q) →F (ii.)...

Let p and q be propositions. (i) Show (p →q) ≡ (p ∧ ¬q) →F (ii.) Why does this equivalency allow us to use the proof by contradiction technique?

Let T∈ L(V), and let p ∈ P(F) be a polynomial. Show that if p(λ) is...

Let T∈ L(V), and let p ∈ P(F) be a polynomial. Show that if p(λ) is an eigenvalue of p(T), then λ is an eigenvalue of T. Under the additional assumption that V is a complex vector space, and conclude that {μ | λ an eigenvalue of p(T)} = {p(λ) | λan eigenvalue of T}.

You are tossing a coin and it has a probability of p to show heads on...

You are tossing a coin and it has a probability of p to show heads on any given toss. You keep on tossing the coin until you see a heads. Let X represent the number of tosses until you see a heads. 1. Find the probability that X is odd. 2. Find the probability that X is even, DO NOT USE QUESTION 1. 3. Let's say the coin is balanced, what is the probability that X is odd? Is this...

In a certain large college course, past records show that grades of A, B, C, D,...

In a certain large college course, past records show that grades of A, B, C, D, and F (which are the only grades assigned) are equally likely. If one student is chosen at random, what is: (a) Pr(C) (b) Pr(A or B) (c) Pr(a grade better than D) (d) Pr(A, B, C, D, or F) (e) Pr(B and D) (f) Pr(E) If two students who do not know one another take the course described above, what are the following probabilities:...

Let (Ω, F , P) be a probability space. Suppose that Ω is the collection of...

Let (Ω, F , P) be a probability space. Suppose that Ω is the collection of all possible outcomes of a single iteration of a certain experiment. Also suppose that, for each C ∈ F, the probability that the outcome of this experiment is contained in C is P(C). Consider events A, B ∈ F with P(A) + P(B) > 0. Suppose that the experiment is iterated indefinitely, with each iteration identical and independent of all the other iterations, until...

USE R CODE AND SHOW OUTPUT APPLIED STATISTICS 2 Traditionally, the policy for students’ course grade,...

USE R CODE AND SHOW OUTPUT APPLIED STATISTICS 2 Traditionally, the policy for students’ course grade, >=90, A; between 80 to 89, B, between 70 to 79, C; between 60-69, D; and F, if <60. Now, suppose we use a new grade policy. We just to separate all students into four parts, with the first parts assigning grade A, second parts assigning grade B, then, C, then D (no F). We use the data RecordMath2526.txt to have a try for...

It is known from past information that the probability of failing to finish an Ironman (called...

It is known from past information that the probability of failing to finish an Ironman (called a DNF) is 15%. Suppose we take a sample of 100 Ironman races over the past few years and find that the DNF percentage is 12%. We are interested in seeing if there has been a significant decrease in the number of DNFs. Use alpha=0.05. Find the 95% confidence interval for the percentage of DNFs. a. (0.0665, 0.1735) b. (0.0555, 0.1845) c. (0.1179, 0.1221)...

Question