Question

In: Statistics and Probability

Suppose the sample space is S = {x| - 8 <= x <= 8}. Let A...

Suppose the sample space is S = {x| - 8 <= x <= 8}. Let A = {x|-2 < x < 2}, B = {x| -3 < x < -1}, and C = {x|1<x<3}. Determine the sets (A intersection B intersection C')'.

Please show work as needed.

Expert Solution

Intersection : The intersection of sets A, B and C is the set of elements that are common to sets A, B and C. It is denoted by A ∩ B ∩ C.

Here, Sample space S = {x| - 8 <= x <= 8} i.e S= {-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8},

A = {x|-2 < x < 2} i.e. A={-1,0,1}, B = {x| -3 < x < -1} i.e. B ={-2} and C = {x|1<x<3} i.e. C = {2}

C' = the set of all elements in the sample space that are not in C = S - C = {-8,-7,-6,-5,-4,-3,-2,-1,0,1,3,4,5,6,7,8}

The set (A intersection B intersection C')' = includes the elements which are not in set (A intersection B intersection C') and the set (A intersection B intersection C') includes the values common in set A , set B and Set C'.

Hence, set (A intersection B intersection C') = = {} , since no elements is common in

set A , set B and Set C'.

Therefore, (A intersection B intersection C')' = = = {-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8}

i.e (A intersection B intersection C')' = = {x| - 8 <= x <= 8}.

orchestra answered 2 years ago

Let X be a compact space and let Y be a Hausdorff space. Let f ∶...

Let X be a compact space and let Y be a Hausdorff space. Let f ∶ X → Y be continuous. Show that the image of any closed set in X under f must also be closed in Y .

Let ? be the sample space of an experiment and let ℱ be a collection of...

Let ? be the sample space of an experiment and let ℱ be a collection of subsets of ?. a) What properties must ℱ have if we are to construct a probability measure on (?,ℱ)? b) Assume ℱ has the properties in part (a). Let ? be a function that maps the elements of ℱ onto ℝ such that i) ?(?) ≥ 0 , ∀ ? ∈ ℱ ii) ?(?) = 1 and iii) If ?1 , ?2 … are...

Sample Spaces 1. Suppose S is a uniform sample space with N elements. If E is...

Sample Spaces 1. Suppose S is a uniform sample space with N elements. If E is any possible come and ω is the probability function for S evaluate ω(e). 2. Define a probability function on the set A = {1, 2, 3} such that A is not a uniform sample space. 3. Given the sample space B = {a, b, c} and probability function ω on B. If ω(a) = 0.3, ω({a, b}) = 0.8 then find ω(b) and ω(c)....

Let S = {s1, s2, s3, s4, s5, s6} be the sample space associated with an...

Let S = {s1, s2, s3, s4, s5, s6} be the sample space associated with an experiment having the probability distribution shown in the accompanying table. If A = {s1, s2} and B = {s1, s5, s6}, find the following. Outcome Probability s1 1 3 s2 1 7 s3 1 6 s4 1 6 s5 1 21 s6 1 7 (a) P(A) = P(B) = (b) P(AC) = P(BC) = (c) P(A ∩ B) = (d) P(A ∪ B) =...

Let X = {Xn:n= 0,1,...,} be a DTMC on state space S. Define Yn = (Xn,...

Let X = {Xn:n= 0,1,...,} be a DTMC on state space S. Define Yn = (Xn, Xn+1). Prove that Y = {Yn: n = 0,1,2,...} is a DTMC. Specify its state space and the transition matrix.

Let V be a Hilbert space. Let f(x) = ∥x∥ for x ∈ V. Using the...

Let V be a Hilbert space. Let f(x) = ∥x∥ for x ∈ V. Using the definition of Frechet differentiation, show that ∇f(x) = x for all x ̸= 0. Furthermore, show that f(x) is not Frechet differentiable at x = 0.

Suppose my sample space consists of current STATS125 students. Let T be the event that a...

Suppose my sample space consists of current STATS125 students. Let T be the event that a randomly selected current STATS125 student usually attends Tuesday lectures, W be the event that a randomly selected current STATS125 student usually attends Wednesday lectures H be the event that a randomly selected current STATS125 student usually attends Thursday lectures. a) Draw 4 Venn diagrams and use shading to identify the following sets: i. T ? H ii. T^complement ? (W ? H) iii. the...

Let A and B be two events in a sample space S. If P(A1Bc) =.10, P(Ac1B)...

Let A and B be two events in a sample space S. If P(A1Bc) =.10, P(Ac1B) =.40 and P(Ac1Bc) =.10, a. Illustrate the events A1Bc, Ac1B and Ac1Bc on a van Venn-diagram b. Check for the independence of events A and B. c. Find P(A1B*AUB).

Let X be a metric space and t: X to X be a map that preserves...

Let X be a metric space and t: X to X be a map that preserves distances: d(t(x), t(y)) = d(x, y). Give an example in whicht is not bijective. Could let t: x to x+1,x non-negative, but how does this mean t is not surjective? Any help will be much appreciated!

Let (X, d) be a metric space. Prove that every metric space (X, d) is homeomorphic...

Let (X, d) be a metric space. Prove that every metric space (X, d) is homeomorphic to a metric space (Y, dY ) of diameter at most 1.