Suppose that a number x is to be selected from the real line R, and let A, B, and C be the events represented by the following subsets of R, where the notation {x : −−−} denotes the set containing every point x for which the property presented following the colon is satisfied: A = {x : 1 ≤ x ≤ 5} B = {x : 3 < x ≤ 7} C = {x : x ≤ 0} Describe each of the following events as a set of real numbers: (a) Ac (b) A ∪ B (c) B ∩ C c (d) (A ∪ B) ∩ C

Q: Let the domain of x and y be all people, Let W(x): "X is a woman". M(y): "y is a man", and L(x.y):…

A: Given W(x): ' x is a woman' M(y):' y is a man'

Q: Write down all elements of {I, J, K} x {W, X}. (Enter your answer in set notation.)…

A: The given problem is to find the Cartesian product of the given sets {I,J,K} and {W,X}.

Q: In this question and subsequently, let d₁, d2, ..., d5 denote the first five digits of your exam…

A: Given : Let d1, d2, d3, d4, d5 denote the first five digit of exam number and X denote the set…

Q: Find the complement of the set given that U = {x | x I and −3 ≤ x ≤ 9}. (Enter your answers as a…

A: First we write U and the set in roaster form.

Q: (2) Is the set {r € Rr² € N} countable? Justify your answer.

A: Yes the set A={x €R : x2 €N } is countable

Q: Suppose a and b are positive integers and 2021 α 2022 2022 b 2023 If s is the minimum value of a+b,…

A:

Q: 6. Suppose that inf A > inf B. a. Show that there exists a € B such that a is a lower bound of A. b.…

A: 6a) Given: Two sets A and B such that infA&gt;infB, To Prove: there exists an element a∈B which is a…

Q: Let A be a subset of real numbers bounded from below. Then, the set-2A = {-2x: x E A} is bounded…

A:

Q: etermine whether the set of x-2x²,2+5x-x²x+x²} is linerly independent in P

A: First we use definition of linearly independent Set and we check given vectors are linearly…

Q: Let A = {1,2} and B = {3, 4}. (a) Find A x B (b) How many subsets Ax B of size 2 are there? List…

A: Given that A= {1, 2} and B= {3, 4}A x B is the cartesian product

Q: Suppose that vehicles taking a particular freeway exit can turn right (R), turn left (L), or go…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: A is the set of odd number greater than 5 and less than 23 n (A)=

A: A is the set of odd numbers greater than 5 and less than  23

Q: Find the complement of the set given that  U = {x | x  I and −3 ≤ x ≤ 9}.  (Enter your answers as a…

A:

Q: In this group of problems, you are given two statements, A and B: determine whether one statement…

A: Solution

Q: Find the complement of the set given that  U = {x | x  I and −3 ≤ x ≤ 5}.  (Enter your answers as a…

A:

Q: Find the complement of the set given that  U = {x | x  I and −3 ≤ x ≤ 10}.  (Enter your answers as a…

A: We Know that,  If U is a universal set and A be any subset of U then the complement of A is the set…

Q: Given a finite set S, find all possible values of |S] so that the set {(a, b) | (a E S) A (b e S) ^…

A:

Q: Let N={1,2,3,4,...}. Let P(x,y) be the predicate that x is less than or equal to y^2

A: (d) S = {1, 2, 3, 4, 5, 6, 7, 8, 9} (e) T = {3,4,5,6,......} (f) R = {} (empty set)Explanation:(d)…

Q: 2. A- (x|x2-2) 8- (x|x< 6) (a) A nc (b) A nB

A: Sets

Q: Let A = (x = R: 7 ≤x < 20} and B = {7, 18, 19, 20, 21). What is A - B? A. {x ER: (7<x< 18) (18 < x…

A:

Q: Determine whether each of the following is a unary operation on the given set. a. h(x) == on N b.…

A: A unary operation is an operation that takes a single input and produces a single output.Then the…

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.