To illustrate the proof of Theorem 1, consider the ran-dom variable X, which takes on the values −2, −1, 0, 1, 2, and 3 with probabilities f(−2), f(−1), f(0), f(1), f(2),and f(3). If g(X) = X2, find(a) g1, g2, g3, and g4, the four possible values of g(x);(b) the probabilities P[g(X) = gi] for i = 1, 2, 3, 4;(c) E[g(X)] = 4i=1gi ·P[g(X) = gi], and show that it equals xg(x)·f(x)

Q: So if g(5) 8 and f(8) 19, then (f o g)(5) = By definition, (f o g)(x) = ?

A: By definition,

Q: f1(x)=√24 and f2(x) = x². √√x³+1 .If (a=0,b= 1), find the probabilities for both functions and then…

A:

Q: x1 x2 x 3 Xx4 +s x1 +x2 x1 x2 +x3 X3 +x4 +x4 = = 1 2 -3

A:

Q: If X(w) 3u-2 find F(z(3t).

A: Note: There is a typo in the choices. To solve this problem, we use the following property.

Q: Let 2 f(x) = a² + 9 and g(x) = /3x – 5 If h(x) = (f o g)(x) and k(x) = (go f)(x) then h(3) and k(3)…

A: Composite functions

Q: - 25х-1 dt 2*

A: Consider ∫25x-12xdx = ∫25x 2-12xdx= ∫25x-x2dx= 12∫24xdx                                     (1) Let…

Q: Discuss the pros and cons of Chebyshev’s rule.

A:

Q: The probability that the majority of a three- person jury will convict a guilty person is given by…

A: The probability that the majority of a three-person jury will convict a guilty person is  given by…

Q: Why does the fact that the orders of the elements of A4 are 1, 2, and3 imply that |Z(A4)| = 1?

A: Given: The orders of the elements of A4 are 1, 2, and 3.We need to signify the given fact to imply…

Q: By definition, (f o g)(x) f(g(x)) ♥ So if g(6) = 9 and f(9) 16, then (f o g)(6) %3D

A:

Q: P(A)=0.02 and p(C)=0.07 determine p(A u C), given that A and C are independent

A: It is given that:And, A and C are independent events.

Q: 4. Use rule of inference to show that if Vx(P9x) → (Q(x) ^ S(x))) and Vx(P(x) ^ R(x)) are true, then…

A: Given: Lets determine∀xPx→Qx∧Sx and ∀xPx∧Rx is true and ∀xRx∧Sx is true using rule of interference.

Q: Find (f 9)(x) if f(æ) = –5æ² + 2æ + 7 and g(x) = x + 1. O (f 9)(x) = 5x + 7 (f 9)(x) = -5x + 7 O (f…

A: Given fx=-5x2+2x+7 and gx=x+1

Q: If A = {2,3} and B = {x|x EZ, x<3}, then A x B = Select one: O a. {(1,2), (1, 3), (2, 2), (2,3)} O…

A: If A=2, 3 and B=x x∈Z+, x&lt;3, then to determine A×B.

Q: If P(x)=x* +ax° + bx? + cx +d and P(1) =P(2)=P(3)=0 then the value of P(4)+P(0) is (A) 28 (B) 4 (C)…

A:

Q: A library subscribes to two different weekly news magazines, each of which is supposed to arrive in…

A: Random Variable: In probability theory, a random variable is a variable whose values depend on…

Q: Given that f(0) = 7, f(1) = –6, f(2) = 15, ƒ(3) = 14, f(4) = –10, and g(0) = 4, g(1) = 3, g(2) = 1,…

A: Given that f(0)=7,f(1)=-6,f(2)=15,f(3)=14,f(4)=-10 g(0)=4,g(1)=3,g(2)=1,g(3)=2,g(4)=0

Q: Let a ER and set fa: R→R: xx+1|-2|2x|+ a. S(a)= {r ER: fa(x)=0}. (So, S(a) is a set). P= {a € R:…

A: Given information fa : ℝ→ℝ  : x→x+1 -22-x +a Sa =  x∈ℝ : fax =0  P =  a∈R : Sa = ϕ Qa =  x∈ℝ : fax…

Q: A particular road is used by N drivers each day. Each driver obtains a benefit v from the journey…

A:

Q: If S = {a, b, c} with P(a) = 8P(b) = 5P(c), find P(a).

A: Total probability:If a sample space contains mutually exclusive and exhaustive events, then the sum…

Q: Let f(x) = 3x – 1 and g(x) = x² + 4x – 2. Evaluate the following. - a. f(3) = 8 b. ƒ( – 1) = |-4 с.…

A:

Q: IF fx) = (1 - x) and g(x) = 9 - x, find fg(x)) and g(fx)). Ag(x)) = 9(Ax)) =

A: Given that:           f(x)=(1-x)2 and g(x)=9-x Find f(g(x)) and g(f(x)).

Q: If C(12,4)+C(12,5) = C(n, 5), then n is equal to

A:

Q: The weather on any given day in a particular city can be sunny, cloudy, or rainy. It has been…

A: Markov Chain: A Markov Chain is a random process describing a sequence of possible events in which…

Q: (a) Let P(B1 N B2) > 0, and A1 U A2 C B1 N B2. Then show that P(A||B1) .P (A2\B2) = P (A||B2) .P…

A: Note: Hey there! Thank you for the question. As you have posted three different questions together,…

Q: Submit You have used 0 of 2 attemp ts Save If A = (1, 4, 9, ., 256), how many elements are in A?…

A:

Q: A computer-consulting firm presently has bids out on two projects. Let A= [awarded project 1] and B=…

A: The condition of two independent events is-PA∩B=PA.PB

Q: LetP(A) = 0.20, P(B) = 0.80, andP(A∩B) = 0.16. Are A and B independent? Justify your result…

A:

Q: Evaluate S(3) if S(r) = 4xr².

A: Given query is to find the value of S(3).

Q: If P(E∩F)=0.042, P(E|F)=0.12, and P(F|E)=0.6, then (a)   P(E)= (b)   P(F)= (c)   ?(?∪?)=

A: It is given that P(E∩F)=0.042, P(E/F)=0.12 and P(F/E)=0.6.

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.