(a) Find px₁,...,xk (X1, X2, · · ·‚ Xk). (b) Find px;(x;) for any 1 ≤ i ≤ k.

Q: (a) Explain with cases why, if a is a real number,  then a ≤ |a|. (b) Explain, if, for any real…

A:

Q: (B1>0 (g) If a > b and c> d, then a + c > b + d. h) If a > b> 0 and c > d > 0, then ac > bd. i) If a…

A: For (f) ,We use a theorem that "if n∈ℤ and n≠0 then n2>0.

Q: 3. Invent two interesting and original positive integers a and b. Let f(x) = ax +3. (a) (b) What is…

A: Given function is fx=ax+3. To find:  a  f10   (b). A number x such that fx=b Solution: Given…

Q: Suppose random variables X and Y are conditionally independent given random variable Z, i.e. P(X,…

A: Given that, P(X, Y|Z) = P(X|Z)P(Y|Z) (a). Then  P(Y/X,Z)= P(Y,X,Z)/P(X,Z)  (X and Y are…

Q: Determine the values of b and c such that the following function is continuous on the entire real…

A:

Q: Determine the threer-value candidates for absolute extremum on the interval [-3,1] for the function…

A:

Q: b) Prove that |x| ≤ 1 implies that |x² + 2x - 3| ≤ 4|x − 1].

A:

Q: Let A = {x € R : x < a} and B={x €R: x < b}, where a and b are real numbers. Show that sup(A+ B) =…

A:

Q: X< 3x +2 < 2x+4

A: The given inequality: x&lt;3x+2&lt;2x+4

Q: If 90% of the athletes who test positive for steroids in fact use them, and 10% of all athletes use…

A:

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: Find the values of m and n such that the function f defined by is continuous. m = Number n= Number…

A: We have to find out

Q: Let f(x) = |x − 2| − 1. i) Make a table of ordered pairs for f(x), for all integers x with −3 ≤ x…

A:

Q: Prove that if |x-1| < 1, then x² - 2x + 5| < 8.

A:

Q: 4. Find all real values of x such that |x-1| > |x+1]. * (-00,-1] (-00,0) [-1,0) [-1,1) None of the…

A:

Q: 6. For each statement below, decide whether that statement is true or false. (a) |N| < |N|U-1 (b)…

A: (a) False. The statement "IN &lt;INU-1" is not valid because "INU-1" is not a recognized notation.…

Q: 5.) Evaluate f(-3) for f(x) = x³ +3x + 17

A: Given  f(x) =x3+3x+17

Q: х — 5, for a 3.

A:

Q: Let f: AB and 9: B→C be defined as follows: f(a) = 4a² +2 and g(b) = 26-7 Compute the following: (a)…

A: Let A=B=C=x|x is a real number Let f:A→B and g:B→C be defined as  fa=4a2+2andgb=2b-7 Hence…

Q: Which of the following does not define relation as a function? Select one: {(x,y) y = (x + 1)²} {(x,…

A:

Q: Suppose that a function ƒ(x) has the property that ƒ(x1 x2) = ƒ(x1) + ƒ(x2) for any two positive…

A:

Q: Suppose X₁ ~ N(6, 1) and X₂ ~ N(7,2), and X₁ is independent of X₂. Find P(X₁ < X₂) and P(X₁ < X₂ +…

A: We know linear combination of normal distribution is also a normal distribution. Therefore any…

Q: Let A =[1 -1]            [2 0] and --->x =[ i]                  [1 + i] . SHOW that Re (A--->x )…

A:

Q: Let P(x) denote the statement "x < 4." P(4) is A) True False

A:

Q: Find: ii) P (X₂ ≤ 1X₂ ≤). f(x₁,x₂) = {1x1x² 0≤x≤1, 0≤ x₂ ≤ 1 elsewhere

A:

Q: Let f(x) = -x4-9x³+2x+8. Find the open intervals on which is concave up (down). Then determine the…

A: For a given function f( x ) ( a ) inflection points by f''( x ) = 0 ( b ) For concave up , f''( x )…

Q: x² – 4 Ax) xx – 2

A:

Q: For what value(s) of x is g(x) ≤ 3? (Enter your answer using interval notation

A: